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Simon, Jonathan

Roots and centralizers of peripheral elements in knot groups. (English) Zbl 0314.55003

Math. Ann. 222, 205-209 (1976).
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Cited in 12 Documents

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M10 Covering spaces and low-dimensional topology
57N10 Topology of general \(3\)-manifolds (MSC2010)
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Full Text: DOI EuDML

References:

[1] Bing, R. H., Martin, J. M.: Cubes with knotted holes. Trans. Amer. Math. Soc.155, 217-231 (1971) · Zbl 0213.25005 · doi:10.1090/S0002-9947-1971-0278287-4
[2] Burde, G., Zieschang, H.: Eine Kennzeichnung der Torusknoten. Math. Ann.167, 169-175 (1966) · Zbl 0145.20502 · doi:10.1007/BF01362170
[3] Feustel, C. D.: Embeddings and essential embeddings of annuli and möbius bands inM 3. preprint · Zbl 0314.55004
[4] Fox, R. H.: A quick trip through knot theory, Topology of 3-Manifolds (M. K. Fort, Ed.). New York: Prentice-Hall 1962 · Zbl 1246.57002
[5] Gonzalez-Acuña, F.: Dehn’s construction on knots. Bol. Soc. Mat. Mex.15, 58-79 (1970) · Zbl 0229.55004
[6] Hempel, J.: A simply connected 3-manifold isS 3 if it is the sum of a solid torus and the complement of a torus knot. Proc. Amer. Math. Soc.15, 154-158 (1964) · Zbl 0118.18802
[7] Jaco, W.: Roots, relations and centralizers in three manifold groups. Geometric Topology (L.C. Glaser and T. B. Rushing, eds), Lecture Notes in Mathematics, 283-310. Berlin, Heidelberg, New York: 1975 · Zbl 0313.55002
[8] Magnus, W., et al.: Combinatorial Group Theory. New York: John Wiley 1966 · Zbl 0138.25604
[9] Noga, D.: Über den Aussenraum von Produktknoten und die Bedeutung der Fixgruppen. Math. Z.101, 131-141 (1967) · Zbl 0183.52102 · doi:10.1007/BF01136030
[10] Schubert, H.: Über eine numerische Knoteninvariante. Math. Z.61, 245-288 (1954) · Zbl 0058.17403 · doi:10.1007/BF01181346
[11] Seifert, H.: Topologie Dreidimensionaler Gefaserter Räume. Acta Math.60, 147-238 (1933) · JFM 59.1241.02 · doi:10.1007/BF02398271
[12] Simon, J.: An algebraic classification of knots inS 3. Ann. Math.97, 1-13 (1973) · Zbl 0256.55003 · doi:10.2307/1970874
[13] Simon, J.: Compactification of covering spaces of compact 3-manifolds. to appear inMichigan Math. J.
[14] Waldhausen, F.: On the determination of some bounded 3-manifolds by their fundamental groups alone. Proc. International Symp. Topology and Appl., Herceg-Novi, Yugoslavia, 1968, Beograd 331-332 (1969)
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