×

Artin braids and the groups and spaces connected with them. (English) Zbl 0479.20016


MSC:

20F36 Braid groups; Artin groups
20-02 Research exposition (monographs, survey articles) pertaining to group theory

Citations:

Zbl 0434.20020
Full Text: DOI

References:

[1] V. I. Arnol’d, ?A remark on the branching of hyperelliptic integrals as functions of the parameters,? Funkts. Analiz Ego Prilozhen.,2, No. 3, 1?3 (1968). · Zbl 0174.45203 · doi:10.1007/BF01075356
[2] V. I. Arnol’d, ?On the braids of algebraic functions and the cohomologies of swallowtails,? Usp. Mat. Nauk,23, No. 4, 247?248 (1968).
[3] V. I. Arnol’d, ?Cohomology ring of the group of dyed braids,? Mat. Zametki,5, No. 2, 227?231 (1969).
[4] V. I. Arnol’d. ?On cohomology classes of algebraic functions preserved under Tschirnhausen transformations,? Funkts. Analiz Ego Prilozhen.,4, No. 1, 84?85 (1970).
[5] V. I. Arnol’d, ?On certain topological invariants of algebraic functions,? Tr. Mosk. Obshch.,21, 27?46 (1970).
[6] V. I. Arnol’d, ?Topological invariants of algebraic functions. II,? Funkts. Analiz Ego Prilozhen.,4, No. 2, 1?9 (1970). · Zbl 0207.03902 · doi:10.1007/BF01075614
[7] V. I. Arnol’d, ?Normal forms of functions close to degenerate critical points, Weyl groups Ak. Dk. Ek. and Lagrange singularities,? Funkts. Analiz Ego Prilozhen.,6, No. 4, 3?25 (1972).
[8] V. I. Arnol’d, ?Critical points of functions and classification of caustics,? Usp. Mat. Nauk,29, No. 3, 243?244 (1974).
[9] V. I. Arnol’d, ?Critical points of smooth functions and their normal forms,? Usp. Mat. Nauk,30, No. 5, 3?65 (1975).
[10] V. I. Arnol’d, ?Critical points of functions on a manifold with boundary, simple Lie groups Bk. Ck. F4. and singularities of evolutes,? Usp. Mat. Nauk,33, No. 5, 91?105 (1978).
[11] N. Bourbaki, Éléments de Mathématique. Fase. XXXIV. Groupes et Algèbres de Lie. Chapitre IV: Groupes de Coxeter et Systèmes de Tits. Chapitre V: Groupes Engendrés par des Réflexions. Chapitre VI: Systèmes de Racines. Hermann et Cie., Paris (1968). · Zbl 0186.33001
[12] N. M. Vainberg, ?On the free equivalence of closed braids,? Dokl. Akad. Nauk SSSR,23, 215?216 (1939).
[13] P. V. Vainshtein, ?Cohomologies of braid groups,? Funkts. Analiz Ego Prilozhen.,12, No. 2, 72?73 (1978). · Zbl 0403.46030 · doi:10.1007/BF01077577
[14] A. N. Varchenko, ?On the branching of multiple integrals depending on parameters,? Funkts. Analiz Ego Prilozhen.,3, No. 4, 79?80 (1969). · doi:10.1007/BF01078281
[15] É. B. Vinberg and O. V. Shvartsman, ?Riemann surfaces,? in: Algebra. Topology. Geometry [in Russian], Vol. 16, Itogi Nauki i Tekh., VINITI Akad. Nauk SSSR, Moscow (1978), pp. 191?245. · Zbl 0445.30032
[16] O. Ya. Viro, ?Links, two-sheeted branching coverings, and braids,? Mat. Sb.,87, No. 2, 216?228 (1972).
[17] E. A. Gorin, ?On the factorization of abstract entire functions,? Usp. Mat. Nauk,25, No. 4, 177?178 (1970).
[18] E. A. Gorin, ?Equations with abstract entire functions in Banach algebras,? in: Materials of Eighth Math. Interinst. Sci. Conf. Far East [in Russian], Khabarovsk (1970), pp. 9?12.
[19] E. A. Gorin, ?Several examples connected with algebraic equations in algebras of functions,? Dokl. Akad. Nauk SSSR,200, No. 2, 273?276 (1971).
[20] E. A. Gorin, ?On certain algebraic equations with holomorphic coefficients,? Usp. Mat. Nauk,27, No. 3, 197?198 (1972).
[21] E. A. Gorin, ?On algebraic equations in algebras of continuous functions,? Rept. Abstr. Sixth All-Union Topol. Conf. [in Russian], Metsniereba, Tbilisi (1972), p. 43.
[22] E. A. Gorin, ?Holomorphic functions on an algebraic manifold and the reducibility of separable polynomials over certain commutative Banach Algebras,? Rept, Abstr. Seventh All-Union Topol. Conf. [in Russian], Minsk (1977), p. 55.
[23] E. A. Gorin, ?Algebraic equations in commutative Banach algebras and related questions,? Zap. Nauchn. Sem. LOMI Akad. Nauk SSSR,81, 58?61 (1978).
[24] E. A. Gorin, ?On the researches of G. E. Shilov on the theory of commutative Banach algebras and their subsequent development, Usp. Mat. Nauk,33, No. 4, 169?189 (1978). · Zbl 0413.46040
[25] E. A. Gorin and V. Ya. Lin, ?Algebraic equatons with continuous coefficients, ?Material Seventh Math. and Seventh. Phys. Interinst. Sci. Conf. Far East [in Russian], Khabarovsk (1968), pp. 10?12.
[26] E. A. Gorin and V. Ya. Lin, ?Braid groups and algebraic equations with continuous coefficients, ?Usp. Mat. Nauk,24, No. 2, 225?226 (L969).
[27] E. A. Gorin and V. Ya. Lin, ?Algebraic equations with continuous coefficients and certain questions in the algebraic theory of braids,? Mat. Sb.,78, No. 4, 579?610 (1969).
[28] E. A. Gorin and V. Ya. Lin, ?On separable polynomials over commutative Banach algebras,? Dokl. Akad. Nauk SSSR,218, No. 3, 505?508 (1974).
[29] E. A. Gorin and C. Sánchez-Fernández, ?On transcendental equations in commutative Banach algegras,? Funkt. Analiz. Ego, Prilozhen.,11, No. 1, 63?64 (1977).
[30] V. V. Goryunov, ?Cohomologies of braid groups of series C and D and certain stratifications,? Funkt. Analiz. Ego Prilozhen.,12, No. 2, 76?77 (1978). · Zbl 0409.20032
[31] S. Zdravkovska, ?Topological classification of polynomial mappings,? Usp. Mat. Nauk,25, No. 4 179?180 (1970).
[32] V. M. Zinde, ?Commutator subgroups of Artin groups,? Usp. Mat. Nauk,30, No. 5, 207?208 (1975).
[33] V. M. Zinde, ?Certain homomorphisms of Artin groups of series Bn and Dn into groups of the same series and into symmetric groups,? Usp. Mat. Nauk,32, No. 1, 189?190 (1977).
[34] V. M. Zinde, ?Analytic properties of spaces of regular orbits of Coxeter groups of serie B and D, ?Funkts. Analiz Ego Prilozhen.,11, No. 1, 69?70 (1977).
[35] V. M. Zinde, ?Homomorphisms of Artin groups of series B and D,? Moscow Univ., Moscow (1977) (Manuscript deposited in VINITI, June 6, 1977, No. 2230-77 Dep.).
[36] V. M. Zinde, ?Holomorphic mappings of spaces of regular orbits of Coxeter groups of series B and D,? Sib. Mat. Zh.,18, No. 5, 1015?1026 (1977).
[37] Yu. V. Zyuzin, ?Algebraic equations with continuous coefficients on uniform spaces,? Vestn. Mosk. Univ., No. 1, 51?53 (1972). · Zbl 0231.46071
[38] Yu. V. Zyuzin, ?Irreducible holomorphic separable polynomials on bouquets of circular annuli,? Usp. Mat. Nauk,29, No. 5, 221?222 (1974).
[39] Yu. V. Zyuzin, ?Irreducible separable polynomials with holomorphic coefficients on a certain class of complex spaces,? Mat. Sb.,102, No. 4, 569?591 (1977).
[40] Yu. V. Zyuzin, ?Separable polynomials over functional algebras,? Author’s abstract of dissertation for the academic degree of Candidate of Phys.-Math. Sciences, Mosk. Gos. Univ., Moscow (1974).
[41] Yu. V. Zyuzin and V-Ya. Lin, ?Nonbranching algebraic extensions of commutative Banach algebras,? Mat. Sb.,91, No. 3, 402?420 (1973).
[42] Sh. I. Kaliman, ?Holomorphic universal covering of the space of polynomials without multiple roots,? Funkts. Analiz Ego Prilozhen.,9, No. 1, 71 (1975). · Zbl 0328.32008 · doi:10.1007/BF01078188
[43] Sh. I. Kaliman, ?Holomorphic endomorphisms of the manifold of complex polynomials with, discriminant 1,? Usp. Mat. Nauk,31, No. 1, 251?252 (1976).
[44] Sh. I. Kaliman, ?Holomorphic universal covering of the space of polynomials without multiple roots,? Teoriya Funktsii, Funkt, Analiz. Ikh Prilozhen., Resp, Nauchn, Sb., No. 28, 25?35 (1977). · Zbl 0449.32001
[45] Sh. I. Kaliman, ?Holomorphic endomorphisms of complex Weyl chambers of series Dn.? Usp. Mat. Nauk,34, No. 2, 201?202 (1979). · Zbl 0429.20042
[46] F. Klein, Vorlesungen über Höhere Geometrie, Dritte Auflage, Verlag von Julius Springer, Berlin (1926).
[47] A. G. Kurosh; Theory of Groups [in Russian.], 3rd aug, ed., Nauka, Moscow (1967). · Zbl 0189.30801
[48] V. Ya. Lin, ?Algebroid functions and holomorphic elements of homotopy groups of a complex manifold,? Dokl. Akad. Nauk SSSR,201, No. 1, 28?31 (1971).
[49] V. Ya. Lin, ?On the representations of a braid group by permutations,? Usp. Mat. Nauk.27, No. 3, 192 (1972).
[50] V. Ya. Lin, ?Algebraic functions with a universal discriminant manifold,? Funkt, Analiz Ego Prilozhen.,6, No. 1, 81?82 (1972).
[51] V. Ya. Lin, ?On the superpositions of algebraic functions,? Funkts. Analiz. Ego Prilozhen.,6, No. 3, 77?78 (1972).
[52] V. Ya. Lin, ?Representations of braids by permutations,? Usp. Mat. Nauk,29, No. 1, 173?174 (1974).
[53] V. Ya. Lin, ?On fourth-degree polynomials over the algebra of continuous functions,? Funkts. Analiz Ego Prilozhen.,8, No. 4, 89?90 (1974). · doi:10.1007/BF01078591
[54] V. Ya. Lin, ?Superpositions of algebraic functions,? Funkts. Analiz Ego Prilozhen.,10, No. 1, 37?45 (1976).
[55] V. Ya. Lin, ?Holomorphic mappings of certain spaces connected with algebraic functions,? Zap. Nauchn. Sem. LOMI Akad. Nauk SSSR,81, 62?65 (1978).
[56] O. V. Lyashko, ?Geometry of bifurcation diagrams,? Usp. Mat. Nauk,34, No. 3, 205?206 (1979). · Zbl 0434.32020
[57] W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Interscience Publishers, New York (1966). · Zbl 0138.25604
[58] G. S. Makanin, ?The conjugacy problem in a braid group,? Dokl. Akad. Nauk SSSR,182, No. 3, 495?496 (1968).
[59] G. S. Makanin, ?On the normalizers of a braid group,? Mat. Sb.,86, No. 2, 171?179 (1971).
[60] A. I. Mal’tsev, ?On an isomorphic representation of infinite groups of matrices,? Mat. Sb.,4, 405?422 (1940).
[61] A. A. Markov, ?Über die freie Äquivalenz der geschlossener Zöpfe,? Mat. Sb.,1, 73?78 (1936).
[62] A. A. Markov, Foundations of the Algebraic Theory of Tresses, Tr. Mat. Inst. Steklov, Vol. 16, Moscow (1945).
[63] H. Neumann, Varieties of Groups, Springer-Verlag, Berlin-Heidelberg-New York (1967). · Zbl 0149.26704
[64] B. I. Plotkin, Automorphism Groups of Algebraic Systems [in Russian], Nauka, Moscow (1966).
[65] D. M. Smirnov, ?On the theory of residually finite groups,? Ukr. Mat. Zh.,15, No. 4, 453?457 (1963).
[66] V. B. Styshnev, ?Extraction of a root in a braid group,? Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 5, 1120?1131 (1978). · Zbl 0422.20024
[67] D. B. Fuks, ?Cohomologies of a braid group mod 2,? Funkts. Analiz Ego Prilozhen.,4, No. 2, 62?73 (1970).
[68] D. B. Fuks, ?Quillenization and Bordism,? Funkts. Analiz Ego Prilozhen.,8, No. 1, 36?42 (1974).
[69] M. Hall, The Theory of Groups, MacMillan Co., New York (1959). · Zbl 0084.02202
[70] S. I. Epshtein, ?Fundamental groups of spaces of collections of relatively prime polynomials,? Funkts. Analiz Ego Prilozhen.,7, No. 1, 90?91 (1973).
[71] J. W. Alexander, ?A lemma on systems of knotted curves,? Proc. Nat. Acad. Sci. U.S.A.,9, 93?95 (1923). · JFM 49.0408.03 · doi:10.1073/pnas.9.3.93
[72] E. Artin, ?Theorie der Zöpfe,? Abh. Math. Sem. Univ. Hamburg,4, 47?72 (1925). · JFM 51.0450.01 · doi:10.1007/BF02950718
[73] E. Artin, ?Theory of Braids,? Ann. Math.,48, No. 1, 101?126 (1947). · Zbl 0030.17703 · doi:10.2307/1969218
[74] E. Artin, ?Braids and permutations,? Ann. Math.,48, No. 3, 643?649 (1947). · Zbl 0030.17802 · doi:10.2307/1969131
[75] E. Artin, ?The theory of braids,? Am. Sci.,38, 112?119 (1950). · Zbl 0599.20045
[76] R. Baer, ?Über Kurventypen auf Flächen,? J. Reine Angew. Math.,156, 231?246 (1927). · JFM 53.0547.01
[77] R. Baer, ?Die Abbildungstypen-Gruppe der orientierbaren geschlossen Flaeche vom Geschlechte 2,? J. Reine Angew. Math.,160, 1?25 (1929).
[78] G. Baumslag, ?Automorphism groups of residually finite groups,? J. London Math. Soc.,38, No. 1, 117?118 (1963). · Zbl 0124.26003 · doi:10.1112/jlms/s1-38.1.117
[79] J. S. Birman, ?Braid groups and their relationship to mapping class groups,? Doctoral Dissertation, New York Univ., New York (1968).
[80] J. S. Birman, ?On braid groups,? Commun. Pure Appl. Math.,22, No. 1, 41?72 (1969). · Zbl 0157.30904 · doi:10.1002/cpa.3160220104
[81] J. S. Birman, ?Mapping class groups and their relationship to braid groups,? Commun. Pure Appl. Math.,22, No. 2, 213?238 (1969). · Zbl 0167.21503 · doi:10.1002/cpa.3160220206
[82] J. S. Birman, ?Nonconjugate braids can define isotopic knots,? Commun. Pure Appl. Math.,22, No. 2, 239?242 (1969). · Zbl 0187.45502 · doi:10.1002/cpa.3160220207
[83] J. S. Birman, ?Automorphisms of the fundamental group of a closed, orientable 2-manifold,? Proc. Am. Math. Soc.,21, No. 2, 351?354 (1969). · Zbl 0175.50103
[84] J. S. Birman, ?Abelian quotients of the mapping class group of a 2-manifold,? Bull. Am. Math., Soc.,76, No. 1, 147?150 (1970). · Zbl 0191.22401 · doi:10.1090/S0002-9904-1970-12406-5
[85] J. S. Birman, ?A normal form in the homeotopy group of a surface of genus 2, with applications to 3-manifolds,? Proc. Am. Math. Soc.,34, No. 2, 379?384 (1972). · Zbl 0253.55001
[86] J. S. Birman, ?Plat representations for link groups,? Commun. Pure Appl. Math.,26, No. 5?6, 673?678 (1973). · Zbl 0266.20027 · doi:10.1002/cpa.3160260509
[87] J. S. Birman, ?Mapping class groups of surfaces: a survey,? in: L. Greenberg (ed.), Discontinuous Groups and Riemann Surfaces, Ann. Math. Studies, No. 79, Princeton Univ. Press, Princeton, NJ (1974), pp. 57?71. · Zbl 0297.57001
[88] J. S. Birman, ?Poincare’s conjecture and the homeotopy group of a closed, orientable 2-manifold,? J. Austral. Math. Soc.,17, No. 2, 214?221 (1974). · Zbl 0282.55003 · doi:10.1017/S1446788700016773
[89] J. S. Birman, Braids, Links, and Mapping Class Groups, Ann. Math. Studies, No. 82, Princeton Univ. Press, Princeton, NJ (1975). · Zbl 0305.57013
[90] J. S. Birman, ?On the stable equivalence of plat representations of knots and links,? Can. J. Math.,28, No. 2, 264?290 (1976). · Zbl 0339.55005 · doi:10.4153/CJM-1976-030-1
[91] J. S. Birman and D. R. J. Chillingworth, ?On the homeotopy group of a nonorientable surface,? Proc. Cambridge Philos. Soc.,71, No. 3, 437?438 (1972). · Zbl 0232.57001 · doi:10.1017/S0305004100050714
[92] J. S. Birman and H. M. Hilden, ?On the mapping class groups of closed surfaces and as covering spaces,? in: L. V. Ahlfors, L. Bers, H. M. Farkas, R. C. Gunning, I. Kra, and H. E. Rauch (eds.), Advances in the Theory of Riemann Surfaces, Ann. Math. Studies, No. 66, Princeton Univ. Press, Princeton, NJ (1971), pp. 81?115. · Zbl 0217.48602
[93] J. S. Birman and H. M. Hilden, ?Lifting and projecting homeomorphisms,? Arch. Math.,23, No. 4, 428?434 (1972). · Zbl 0247.55001 · doi:10.1007/BF01304911
[94] J. S. Birman and H. M. Hilden, ?Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin’s braid group,? Bull. Am. Math. Soc.,78, No. 6, 1002?1004 (1972). · Zbl 0255.57002 · doi:10.1090/S0002-9904-1972-13082-9
[95] J. S. Birman and H. M. Hilden, ?On isotopies of homeomorphisms of Riemann surfaces,? Ann. Math.,97, No. 3, 424?439 (1973). · Zbl 0237.57001 · doi:10.2307/1970830
[96] J. S. Birman and H. M. Hilden, ?The homeomorphism problem for S3? Bull. Am. Math. Soc.,79, No. 5, 1006?1009 (1973). · Zbl 0272.57001 · doi:10.1090/S0002-9904-1973-13303-8
[97] J. S. Birman and H. H. Hilden, ?Heegaard splittings of branched coverings of S3.? Trans. Am. Math. Soc.,213, 315?352 (1975). · Zbl 0312.55004
[98] J. S. Birman and W. Magnus, ?Discriminant and projective invariants of binary forms,? Commun. Pure Appl. Math.,23, No. 3, 269?275 (1970). · Zbl 0189.55002 · doi:10.1002/cpa.3160230303
[99] F. Bohnenblust, ?The algebraic braid group,? Ann. Math.,48, No. 1, 127?136 (1947). · Zbl 0030.17801 · doi:10.2307/1969219
[100] E. Brieskorn, ?Sur les groupes de tresses [d’après V. I. Arnol’d],? in: Séminaire Bourbaki, Vol. 1971/72, Exposés 400-417, Lect. Notes Math., Vol. 317, Springer-Verlag, Berlin-Heidelberg-New York (1973), pp. 21?44.
[101] E. Brieskorn, ?Die fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe,? Invent. Math.,12, No. 1, 57?61 (1971). · Zbl 0204.56502 · doi:10.1007/BF01389827
[102] E. Brieskorn and K. Saito, ?Artin-Gruppen und Coxeter-Gruppen,? Invent. Math.,17, No. 4, 245?271 (1972). · Zbl 0243.20037 · doi:10.1007/BF01406235
[103] W. Burau, ?Über Zopfinvarianten,? Abh. Math. Sem. Univ. Hamburg,9, 117?124 (1932). · Zbl 0006.03401 · doi:10.1007/BF02940634
[104] W. Burau, ?Über Zopfgruppen und gleichsinning verdrillte Verkettungen,? Abh. Math. Sem. Univ. Hamburg,11, 179?186 (1935). · Zbl 0011.17801 · doi:10.1007/BF02940722
[105] W. Burau, ?Über Verkettungsgruppen,? Abh. Math. Sem. Univ. Hamburg,11, 171?178 (1935). · JFM 61.1021.02 · doi:10.1007/BF02940721
[106] G. Burde, ?Zur Theorie der Zöpfe,? Math. Ann.,151, No. 2, 101?107 (1963). · Zbl 0112.38604 · doi:10.1007/BF01344172
[107] G. Burde, ?Über Normalisatoren der Zopfgruppen,? Abh. Math. Sem. Univ. Hamburg,27, No. 1?2, 97?115 (1964). · Zbl 0134.43104 · doi:10.1007/BF02993060
[108] G. Burde and K. Murasugi, ?Links and Seifert fiber spaces,? Duke Math. J.,37, No. 1, 89?93 (1970). · Zbl 0195.54003 · doi:10.1215/S0012-7094-70-03713-0
[109] W.-L. Chow, ?On the algebraic braid group,? Ann. Math.,49, No. 3, 654?658 (1948). · Zbl 0033.01002 · doi:10.2307/1969050
[110] D. B. Cohen, ?The Hurwitz monodromy group,? J. Algebra,32, No. 3, 501?517 (1974). · Zbl 0343.20002 · doi:10.1016/0021-8693(74)90155-0
[111] D. I. A. Cohen, ?On representations of the braid group,? J. Algebra,7, No. 2, 145?151 (1967). · Zbl 0178.01604 · doi:10.1016/0021-8693(67)90051-8
[112] F. R. Cohen, ?Braid orientations and bundles with flat connections,? Invent. Math.,46, No. 2, 99?110 (1978). · Zbl 0377.55008 · doi:10.1007/BF01393249
[113] F. R. Cohen, T. J. Lada, and J. P. May, The Homology of Iterated Loop Spaces, Lect. Notes Math., Vol. 533, Springer-Verlag, Berlin-Heidelberg-New York (1976). · Zbl 0334.55009
[114] T. M. Cowan, ?The theory of braids and the analysis of impossible figures,? J. Math. Psychol.,11, No. 3, 190?212 (1974). · Zbl 0298.68073 · doi:10.1016/0022-2496(74)90018-2
[115] D. M. Dahm, ?A generalization of braid theory,? Doctoral Dissertation, Princeton Univ., Princeton, NJ (1962).
[116] M. Dehn, ?Die Gruppe der Abbildungsklassen,? Acta Math.,69, 135?206 (1838). · Zbl 0019.25301 · doi:10.1007/BF02547712
[117] P. Deligne, ?Les immeubles des groupes de tresses généralisés,? Invent. Math.,17, No. 4, 273?302 (1972). · Zbl 0238.20034 · doi:10.1007/BF01406236
[118] E. Dyer and R. K. Lashof,? Homology of iterated loop spaces,? Am. J. Math.,84, No, 1, 35?88 (1962). · Zbl 0119.18206 · doi:10.2307/2372804
[119] M. Engber, ?A strengthening of centerlessness in Teichmüller theory,? Proc. Am. Math. Soc.,60, 144?148 (1976). · Zbl 0347.32012
[120] E. Fadell, ?Homotopy groups of configuration spaces and the string problem of Dirac,? Duke Math. J.,9, No. 2, 231?242 (1962). · Zbl 0122.17803 · doi:10.1215/S0012-7094-62-02924-1
[121] E. Fadell and L. Neuwirth, ?Configuration spaces,? Math. Scand.,10, No. 1, 111?118 (1962). · Zbl 0136.44104 · doi:10.7146/math.scand.a-10517
[122] E. Fadell and J. Van Buskirk, ?On the braid groups of E2 and S2.? Bull. Am. Math. Soc.,67, No. 2, 211?213 (1961). · Zbl 0117.41003 · doi:10.1090/S0002-9904-1961-10570-3
[123] E. Fadell and J. Van Buskirk, ?The braid groups of E2 and S2.? Duke Math. J.,29, No. 2, 243?257 (1962). · Zbl 0122.17804 · doi:10.1215/S0012-7094-62-02925-3
[124] R. H. Fox and L. Neuwirth, ?The braid groups,? Math. Scand.,10, No. 1, 119?126 (1962). · Zbl 0117.41101 · doi:10.7146/math.scand.a-10518
[125] R. Fricke and E. Klein, Vorlesungen über die Theorie der automorphen Funktionen. Band I: Die Gruppentheoretischen Grundlagen. Teubner, Stuttgart (1897); Johnson Reprint Corp., New York (1965). · JFM 28.0334.01
[126] W. Fröhlich, ?Über ein spezielles Transformationsproblem bei einer besonderen Klasse von Zöpfen,? Monatsh. Math. Phys.,44, 225?237 (1936). · JFM 62.0658.02 · doi:10.1007/BF01699317
[127] F. A. Garside, ?The theory of knots and associated problems,? Doctoral Dissertation, Oxford Univ., Oxford (1965).
[128] F. A. Garside, ?The braid group and other groups,? Q. J. Math.,20, No. 78, 235?254 (1969). · Zbl 0194.03303 · doi:10.1093/qmath/20.1.235
[129] B. J. Gassner, ?On braid groups,? Abh. Math. Sem. Univ. Hamburg,25, No. 1?2, 10?22 (1961). · Zbl 0111.03002 · doi:10.1007/BF02992772
[130] R. Gillette and J. Van Buskirk, ?The word problem and consequences for the braid groups and mapping class groups of the 2-sphere,? Trans. Am. Math. Soc.,131, No. 2, 277?296 (1968). · Zbl 0169.55303
[131] J. Gilman, ?An example about normalizers in mapping class groups,? Proc. Am. Math. Soc.,69, No. 1, 115?118 (1978). · Zbl 0385.20025 · doi:10.1090/S0002-9939-1978-0486493-0
[132] C. H. Goldberg, ?An exact sequence of braid groups,? Math. Scand.,33, No. 1, 69?82 (1973). · Zbl 0285.57002 · doi:10.7146/math.scand.a-11472
[133] D. L. Goldsmith, ?Motions of links in the 3-sphere,? Doctoral Dissertation, Princeton Univ., Princeton, NJ (1972).
[134] D. L. Goldsmith, ?Homotopy of braids?in answer to a question of E. Artin,? in: R. F. Dickman, Jr. and P. Fletcher (eds.), Topology Conference, Lect. Notes Math., Vol. 375, Springer-Verlag, Berlin-Heidelberg-New York (1974), pp. 91?96.
[135] D. L. Goldsmith, ?Motions of links in the 3-sphere,? Bull. Am. Math. Soc.,80, No. 1, 62?66 (1974). · Zbl 0275.55003 · doi:10.1090/S0002-9904-1974-13353-7
[136] E. K. Grossman, ?On the residual finiteness of certain mapping class groups,? J. London Math. Soc.,9, No. 1, 160?164 (1974). · Zbl 0292.20032 · doi:10.1112/jlms/s2-9.1.160
[137] E. K. Grossman, ?On certain permutation representations of mapping class groups,? Math. Z.,146, No. 2, 105?112 (1976). · Zbl 0298.20026 · doi:10.1007/BF01187699
[138] H. M. Hilden, ?Generators for two groups related to the braid group,? Pacif. J. Math.,59, No. 2, 475?486 (1975). · Zbl 0317.57005 · doi:10.2140/pjm.1975.59.475
[139] A. Hurwitz, ?Über Riemann’sche Flächen mit gegebenen Verzweigungspunkten,? Math. Ann.,39, 1?61 (1891). · JFM 23.0429.01 · doi:10.1007/BF01199469
[140] T. Kaneto, ?On isotopy groups of holed spheres,? Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, No. 347?365, 46?51 (1975). · Zbl 0339.57013
[141] T. Kaneto, ?On isotopy groups of simply connected holed manifolds,? Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, No. 347?365, 52?58 (1975). · Zbl 0339.57014
[142] Y. Ladegaillerie, ?Groupes de tresses et problème des mots dans les groupes de tresses,? Bull. Sci. Math.,100, No. 3, 255?267 (1976). · Zbl 0334.57008
[143] Y. Ladegaillerie, ?Decoupes et isotopies de surfaces topologiques,? Thèse Doct. Sci. Math., Univ. Sci. et Techn. Langudoc, Langudoc (1976).
[144] H. Levinson, ?Decomposable braids,? Doctoral Dissertation, New York Univ., New York (1971).
[145] H. Levinson, ?Decomposable braids and linkages,? Trans. Am. Math. Soc.,178, 111?126 (1973). · Zbl 0275.55002 · doi:10.1090/S0002-9947-1973-0324684-X
[146] H. Levinson, ?Decomposable braids as subgroups of braid groups,? Trans. Am. Math. Soc.,202, 51?55 (1975). · Zbl 0305.55002 · doi:10.1090/S0002-9947-1975-0362287-3
[147] A. Libgober, ?On the fundamental group of the space of cubic surfaces,? Math. Z.,162, No. 1, 63?67 (1978). · Zbl 0368.14010 · doi:10.1007/BF01437823
[148] W. B. R. Lickorish, ?Homomorphisms of nonorientable two-manifolds,? Proc. Cambridge Philos. Soc.,59, No. 2, 307?317 (1963). · Zbl 0115.40801 · doi:10.1017/S0305004100036926
[149] W. B. R. Lickorish, ?A finite set of generators for the homeotopy group of a 2-manifold,? Proc. Cambridge Philos. Soc.,60, No. 4, 769?778 (1964). · Zbl 0131.20801 · doi:10.1017/S030500410003824X
[150] W. B. R. Lickorish, ?On the homeotopy group of a 2-manifold (corrigendum),? Proc. Cambridge Philos. Soc.,62, No. 4, 679?681 (1966). · Zbl 0145.44102 · doi:10.1017/S0305004100040330
[151] S. Lipschutz, ?On a finite matrix representation of the braid group,? Arch. Math.,12, No. 1, 7?12 (1961). · Zbl 0134.26001 · doi:10.1007/BF01650516
[152] S. Lipschutz, ?Ntate on a paper by Shepperd on the braid group,? Proc. Am. Math. Soc.,14, No. 2, 225?227 (1963). · doi:10.1090/S0002-9939-1963-0146830-2
[153] E. Looijenga, ?The complement of the bifurcation variety of a simple singularity,? Invent. Math.,23, No. 2, 105?116 (1974). · Zbl 0278.32008 · doi:10.1007/BF01405164
[154] C. Maclachlan, ?On a conjecture of Magnus on the Hurwitz monodromy group,? Math. Z.,132, No. 1, 45?50 (1973). · Zbl 0255.30006 · doi:10.1007/BF01214032
[155] C. Maclachlan, ?Note on the Hurwitz-Nielsen realization problem,? Proc. Am. Math. Soc.,64, No. 1, 87?90 (1977). · Zbl 0364.32007 · doi:10.1090/S0002-9939-1977-0442928-X
[156] C. Maclachlan, ?On representations of Artin’s braid group,? Mich. Math. J.,25, No. 2, 235?244 (1978). · Zbl 0366.20032 · doi:10.1307/mmj/1029002065
[157] C. Maclachlan and W. J. Harvey, ?On mapping-class groups and Teichmüller spaces,? Proc. London Math. Soc.,30, No. 4, 496?512 (1975). · Zbl 0303.32020 · doi:10.1112/plms/s3-30.4.496
[158] W. Magnus, ?Über Automorphismen von Fundamentalgruppen berandeter Flachen,? Math. Ann.,109, No. 5, 617?646 (1934). · JFM 60.0091.01 · doi:10.1007/BF01449158
[159] W. Magnus,? Residually finite groups,? Bull. Am. Math. Soc.,75, No. 2, 305?316 (1969). · Zbl 0196.04704 · doi:10.1090/S0002-9904-1969-12149-X
[160] W. Magnus, ?Braids and Riemann surfaces,? Commun. Pure Appl. Math.,25, No. 2, 151?161 (1972). · Zbl 0231.55004 · doi:10.1002/cpa.3160250205
[161] W. Magnus, ?Braid groups: a survey,? in: M. F. Newman (ed.), The Theory of Groups, Lect. Notes Math., Vol. 372, Springer-Verlag, Berlin-Heidelberg-New York (1974), pp. 463?487.
[162] W. Magnus, ?Two generator subgroups of PSL(2,C),? Nachr. Akad. Wiss, Göttingen, Math. Phys. Kl., II, No. 7, 1?14 (1975). · Zbl 0312.20031
[163] W. Magnus and A. Peluso, On knot groups,? Commun. Pure Appl. Math.,20, No, 4, 749?770 (1967). · Zbl 0164.54102 · doi:10.1002/cpa.3160200407
[164] W. Magnus and A. Peluso, ?On a theorem of V. I. Arnol’d,? Commun. Pure Appl. Math.,22, No. 5, 683?692 (1969). · Zbl 0184.49001 · doi:10.1002/cpa.3160220508
[165] W. Mangier, ?Die Klassen von topologischen Abbildungen einer geschlossenen Flache auf sich,? Math. Z.,44, No. 4, 541?554 (1939). · Zbl 0019.28203 · doi:10.1007/BF01210672
[166] G. S. McCarthy, Jr., ?Homeotopy groups,? Trans. Am. Math. Soc.,106, No. 2, 293?304 (1963). · doi:10.1090/S0002-9947-1963-0145531-9
[167] J. W. Milnor, ?Link groups,? Ann. Math.,59, No. 2, 177?195 (1954). · Zbl 0055.16901 · doi:10.2307/1969685
[168] J. W. Milnor, ?Isotopy of links,? in: R. H. Fox, D. C. Spencer, and A. W. Tucker (eds.), Algebraic Geometry and Topology: A Symposium in Honor of S. Lefschetz, Princeton Univ. Press, Princeton, N. J. (1957), pp. 280?306. · Zbl 0080.16901
[169] K. Murasugi, On Closed 3-Braids, Mem. Am. Math. Soc., No. 151, Am. Math. Soc., Providence, RI (1974). · Zbl 0327.55001
[170] K. Murasagi, ?On the divisibility of knot groups,? Pacif. J. Math.,52, No. 2, 491?503 (1974). · Zbl 0312.20020 · doi:10.2140/pjm.1974.52.491
[171] K. Murasugi, ?Seifert fiber spaces and braid groups,? Preprint, Toronto (1979). · Zbl 0489.57003
[172] K. Murasugi and R. S. D. Thomas, ?Isotppic closed nonconjugate braids,? Proc. Am. Math. Soc.,33, No. 1, 137?139 (1972). · Zbl 0232.55003 · doi:10.1090/S0002-9939-1972-0292061-0
[173] M. H. A. Newman, ?On a string problem of Dirac,? J. London Math. Soc.,17, No. 3, 173?177 (1942). · Zbl 0028.09403 · doi:10.1112/jlms/s1-17.3.173
[174] J. Nielsen,? Über topologische Abbildungen geschlossener Flächen,? Abh. Math. Sem. Univ. Hamburg,3, 246?260 (1924). · JFM 50.0660.02 · doi:10.1007/BF02954627
[175] J. Nielsen, ?Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, I?III,? Acta Math.,50, 189?358 (1927);53, 1?76 (1929);58, 87?167 (1931). · JFM 53.0545.12 · doi:10.1007/BF02421324
[176] J. Powell, ?Two theorems on the mapping class group of a surface,? Proc. Am. Math. Soc.,68, No. 3, 347?350 (1978). · Zbl 0391.57009 · doi:10.1090/S0002-9939-1978-0494115-8
[177] L. V. Quintas, ?Solved and unsolved problems in the computation of homeotopy groups of 2-manifolds,? Trans. N. Y. Acad. Sci.,30, No. 7, 919?938 (1968). · Zbl 0307.57015 · doi:10.1111/j.2164-0947.1968.tb02535.x
[178] G. P. Scott, ?The space of homeomorphisms of a 2-manifold,? Topology,9, No. 1, 97?109 (1970). · Zbl 0174.26305 · doi:10.1016/0040-9383(70)90053-4
[179] G. P. Scott, ?Braid groups and the group of homeomorphisms of a surface,? Proc. Cambridge Philos. Soc.,68, No. 3, 605?617 (1970). · Zbl 0203.56302 · doi:10.1017/S0305004100076593
[180] G. B. Segal, ?Configuration-spaces and iterated loop-spaces,? Invent. Math.,21, No. 3, 213?221 (1973). · Zbl 0267.55020 · doi:10.1007/BF01390197
[181] J. A. H. Shepperd, ?Braids which can be plaited with their threads tied together at each end,? Proc. R. Soc.,A265, No. 1321, 229?244 (1962). · Zbl 0103.39504 · doi:10.1098/rspa.1962.0006
[182] N. Smythe, ?Isotopy invariants of links,? Doctoral Dissertation, Princeton Univ., Princeton, NJ (1965).
[183] D. J. Sprows, ?Homeotopy groups of compact 2-manifolds,? Fund, Math.,90, No. 1, 99?103 (1975).
[184] R. S. D. Thomas, ?An algorithm for combing braids,? Proc. 2nd Louisiana Conf, Combinatorics, Graph Theory, and Computing, Baton Rouge, LA (1971), pp. 517?532. · Zbl 0289.20021
[185] R. S. D. Thomas, ?Partially closed braids,? Can. Math. Bull.,17, No. 1, 99?107 (1974). · Zbl 0306.55002 · doi:10.4153/CMB-1974-018-8
[186] R. S. D. Thomas, ?The structure of the fundamental braids,? Q. J. Math.,26, No. 103, 283?288 (1975). · Zbl 0313.20018 · doi:10.1093/qmath/26.1.283
[187] R. S. D. Thomas and B. T. Paley, ?Garside’s braid-conjugacy solution implemented,? Util. Math.,6, 321?335 (1974). · Zbl 0294.55002
[188] J. Tits, ?Le problème des mots dans les groupes de Coxeter,? Symposia Mathematica, Vol. I, Academic Press Inc. (London) Ltd., London-New York (1969), pp. 175?185. · Zbl 0206.03002
[189] J. Van Buskirk, ?Braid groups of compact 2-manifolds with elements of finite order,? Trans. Am. Math. Soc.,122, No. 1, 81?97 (1966). · Zbl 0138.19103
[190] H. Zieschang, ?On the homeotopy groups of surfaces,? Math. Ann.,206, No. 1, 1?21 (1973). · Zbl 0248.55001 · doi:10.1007/BF01431525
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.