Topology. Abstracts from the workshop held July 24–30, 2022. (Topologie.) (English) Zbl 1520.00018
Summary: The lectures in the workshop covered various topics in modern topology, including algebraic and geometric topology, homotopy theory, geometric group theory, and manifold topology, as well as connections to neighboring areas, most prominently symplectic topology/geometry. The following current research topics received more attention during the workshop: manifolds and K-theory, symplectic topology and Floer homology, generalizations of hyperbolic techniques in geometric group theory, and equivariant and motivic homotopy theory. The aim of the various topics was to foster communication and provide chances for participants to see and experience driving questions and important methods in nearby fields within the realm of topology.
MSC:
| 00B05 | Collections of abstracts of lectures |
| 00B25 | Proceedings of conferences of miscellaneous specific interest |
| 55-06 | Proceedings, conferences, collections, etc. pertaining to algebraic topology |
| 57-06 | Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes |
References:
| [1] | M. Abouzaid, A. Blumberg. Arnol’d conjecture and Morava K-theory. Preprint, available at 2103.01507. |
| [2] | M. Abouzaid, M. McLean and I. Smith. Complex cobordism, Hamiltonian loops and global Kuranishi charts. Preprint, available at arXiv:2110.14320. |
| [3] | M.-C. Cheng. Poincaré duality in Morava K-theory for classifying spaces of orbifolds. Preprint, available at arXiv:1305.2731. |
| [4] | J. Greenlees and H. Sadofsky. The Tate spectrum of vn-periodic complex oriented theories. Math. Zeit., 222(3):391-405, 1996. · Zbl 0849.55005 |
| [5] | M. Hovey. Bousfield localization functors and Hopkins’ chromatic splitting conjecture. In The Cech centennial (Boston, MA, 1993), volume 181 of Contemp. Math., pages 225-250. Amer. Math. Soc., Providence, RI, 1995. · Zbl 0830.55004 |
| [6] | F. Lalonde, D. McDuff and L. Polterovich. Topological rigidity of Hamiltonian loops and quantum homology. Invent. Math. 135:369-385, 1999. References · Zbl 0907.58004 |
| [7] | R. Reis and M. Weiss, Smooth maps to the plane and Pontryagin classes Part I: Local aspects, Port. Math. 69 (2012), no. 1, 41-67. · Zbl 1266.58022 |
| [8] | R. Reis and M. Weiss, Functor calculus and the discriminant method, Q. J. Math. 65 (2014), no. 3, 1069-1110. · Zbl 1303.57021 |
| [9] | R. Reis and M. Weiss, Rational Pontryagin classes and functor calculus, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 8, 1769-1811. · Zbl 1353.57026 |
| [10] | M. Weiss, Rational Pontryagin classes of Euclidean fiber bundles, Geom. Topol. 25 (2021), no. 7, 3351-3424. · Zbl 1491.57021 |
| [11] | A. Kupers, Some finiteness results for groups of automorphisms of manifolds, Geom. Topol. 23 (2019), no. 5, 2277-2333. · Zbl 1437.57035 |
| [12] | O. Randal-Williams, The family signature theorem, arXiv:2204.11696. References |
| [13] | I. Chatterji and C. Drutu Median geometry for spaces with measured walls and for groups. Preprint 2017, recently updated. |
| [14] | I. Chatterji, C. Druţu, and F. Haglund, Kazhdan and Haagerup properties from the median viewpoint, Adv. in Mathematics 225 (2010), 882-921. · Zbl 1271.20053 |
| [15] | I. Chatterji, T. Fernós, and A. Iozzi, with an appendix by P.-E. Caprace, The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes, Journal of Topology 9 (2016), 349-400. · Zbl 1387.20032 |
| [16] | V. Chepoi, Graphs of Some CAT(0) Complexes, Adv. in Appl. Math. 24 (2000), 125-179. · Zbl 1019.57001 |
| [17] | E. Fioravanti, Superrigidity of actions on finite-rank median spaces, Adv. Math. 352 (2019), 1206-1252. · Zbl 1454.20085 |
| [18] | G. Niblo, N. Wright and J. Zhang, Coarse median algebras: The intrinsic geometry of coarse median spaces and their intervals, Selecta Mathematica (N.S.) 27 (2021), Paper No. 20, 50. · Zbl 1535.20220 |
| [19] | H. Petyt, Mapping Class Groups are quasicubical, preprint https://arxiv.org/2112.10681. References |
| [20] | M. Bestvina and K.Fujiwara, Bounded cohomology of subgroups of mapping class groups. Geom. Topol. 6 (2002) 69-89. · Zbl 1021.57001 |
| [21] | J. Bowden, S. Hensel and R. Webb, Quasi-morphisms on surface diffeomorphism groups, J. Amer. Math. Soc. 35 (2022), 211-231. · Zbl 1511.20151 |
| [22] | J. Bowden, K. Mann, E. Militon, S. Hensel and R. Webb, Rotation sets and actions on curves (to appear in Adv. Math.). · Zbl 1507.37061 |
| [23] | D. Burago, S. Ivanov, and L. Polterovich, Conjugation-invariant norms on groups of geo-metric origin, in Groups of diffeomorphisms, volume 52 of Adv. Stud. Pure Math., pp. 221-250. Math. Soc. Japan, Tokyo, 2008. · Zbl 1222.20031 |
| [24] | John L. Harer, Stability of the homology of the mapping class groups of orientable surfaces Ann. of Math. (2), 121(2):215-249, 1985. · Zbl 0579.57005 |
| [25] | H.Masur and Y. Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math., 138, (1999) 103-149. · Zbl 0941.32012 |
| [26] | T. Tsuboi. On the uniform perfectness of diffeomorphism groups, in Groups of diffeomor-phisms, volume 52 of Adv. Stud. Pure Math., pages 505-524. Math. Soc. Japan, Tokyo, 2008. · Zbl 1183.57024 |
| [27] | T. Tsuboi, On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds, Comment. Math. Helv., 87, 141-185, 2012. · Zbl 1236.57039 |
| [28] | W. J. Harvey, Boundary structure of the modular group. In Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), volume 97 of Ann. of Math. Stud., pp. 245-251. Princeton Univ. Press, Princeton, N.J., 1981. · Zbl 0461.30036 |
| [29] | I. Dai, J. Hom, M. Stoffregen, and L. Truong, An infinite-rank summand of the homology cobordism group, preprint, arXiv:1810.06145, 2018. |
| [30] | K. Hendricks and C. Manolescu, Involutive Heegaard Floer homology, Duke Math. J. 166, no. 7 (2017), 1211-1299. · Zbl 1383.57036 |
| [31] | K. Hendricks, J. Hom, M. Stoffregen, and I. Zemke, Surgery exact triangles in involutive Heegaard Floer homology,, preprint, arXiv:2011.00113, 2020. |
| [32] | K. Hendricks, J. Hom, M. Stoffregen, and I. Zemke, On the quotient of the homology cobor-dism group by Seifert spaces, preprint, arXiv:2103.04363, 2021. References |
| [33] | M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math., 129(3):445-470, 1997. · Zbl 0888.20021 |
| [34] | M. Bestvina and M. Handel, Train tracks and automorphisms of free groups, Ann. of Math. (2), 135(1):1-51, 1992. · Zbl 0757.57004 |
| [35] | J. Hahn and A. Raksit and D. Wilson A motivic filtration on the topological cyclic homology of commutative ring spectra, arXiv:22206.11208. |
| [36] | B. Morin, Topological Hochschild homology and Zeta-values, arXiv:2011.11549. |
| [37] | B. Bhatt and J. Lurie, Absolute prismatic cohomology, arXiv:2201.06120. |
| [38] | B. Bhatt and M. Morrow and P. Scholze, Topological Hochschild homology and integral p-adic Hodge theory, Publ. Math. Inst. HautesÉtudes Sci. 129 (2019), 199-310. · Zbl 1478.14039 |
| [39] | Emmanuel Ferrand. On a theorem of Chekanov. In Symplectic singularities and geom-etry of gauge fields (Warsaw, 1995), volume 39 of Banach Center Publ., pages 39-48. Polish Acad. Sci. Inst. Math., Warsaw, 1997. · Zbl 0893.53015 |
| [40] | Kiyoshi Igusa. The stability theorem for smooth pseudoisotopies. K-Theory, 2(1-2):vi+355, 1988. · Zbl 0691.57011 |
| [41] | Friedhelm Waldhausen. Algebraic K-theory of spaces, a manifold approach. In Current trends in algebraic topology, Part 1 (London, Ont., 1981), volume 2 of CMS Conf. Proc., pages 141-184. Amer. Math. Soc., Providence, R.I., 1982. · Zbl 0595.57026 |
| [42] | Friedhelm Waldhausen, Björn Jahren, and John Rognes. Spaces of PL manifolds and categories of simple maps, volume 186 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2013. · Zbl 1309.57001 |
| [43] | M. Chas and D. Sullivan. String topology. Preprint 1999 (arXiv:math.GT/9911159). |
| [44] | R. Cohen, J. Klein and D. Sullivan. The homotopy invariance of the string topology loop product and string bracket. J. Topol., 1(2):391-408, 2008. · Zbl 1146.55002 |
| [45] | N. Hingston and N. Wahl. Products and coproducts in string topology, to appear in Ann. Sci.Éc. Norm. Supér. |
| [46] | A. Klamt, Natural operations on the Hochschild complex of commutative Frobenius algebras via the complex of looped diagrams. Preprint 2013 (arXiv:1309.4997). |
| [47] | F. Naef. The string coproduct “knows” reidemeister/whitehead torsion. Preprint 2021. (arXiv:2106.11307). |
| [48] | F. Naef, M. Rivera and N. Wahl. String topology in three flavours. Preprint 2022 (arXiv:2203.02429). |
| [49] | F. Naef and Th. Willwacher, String topology and configuration spaces of two points. Preprint 2019. (arXiv:1911.06202). |
| [50] | D. Sullivan. Open and closed string field theory interpreted in classical algebraic topology. In Topology, geometry and quantum field theory, volume 308 of London Math. Soc. Lecture Note Ser., pages 344-357. Cambridge Univ. Press, Cambridge, 2004. · Zbl 1088.81082 |
| [51] | N. Wahl. Universal operations in Hochschild homology. J. Reine Angew. Math., 720:81-127, 2016. · Zbl 1362.16010 |
| [52] | N. Wahl and C. Westerland. Hochschild homology of structured algebras. Adv. Math., 288:240-307, 2016. · Zbl 1329.55009 |
| [53] | H. Bass, M. Lazard and J.-P. Serre, Sous-groupes d’indice fini dans SL(n, Z), Bull. Amer. Math. Soc. 70 (1964), 385-392. · Zbl 0232.20086 |
| [54] | A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci.École Norm. Sup. (4) 7 (1974), 235-272 (1975). · Zbl 0316.57026 |
| [55] | A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436-491. · Zbl 0274.22011 |
| [56] | T. Brendle, N. Broaddus, and A. Putman, The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary to appear in Israel J. Math. arXiv:2003.10913 |
| [57] | M. R. Bridson and K. Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, in Problems on mapping class groups and related topics, 301-316, Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI. arXiv:math/0507612 · Zbl 1184.20034 |
| [58] | R. M. Charney, Homology stability for GLn of a Dedekind domain, Invent. Math. 56 (1980), no. 1, 1-17. · Zbl 0427.18013 |
| [59] | R. Charney, On the problem of homology stability for congruence subgroups, Comm. Algebra 12 (1984), no. 17-18, 2081-2123. · Zbl 0542.20023 |
| [60] | T. Church, B. Farb and A. Putman, The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension, Int. Math. Res. Not. IMRN 2012, no. 21, 5025-5030. arXiv:1108.0622 · Zbl 1260.57033 |
| [61] | A. Fathi, F. Laudenbach and V. Poénaru, Thurston’s work on surfaces, Mathematical Notes, 48, Princeton University Press, Princeton, NJ, 2012. · Zbl 1244.57005 |
| [62] | N. J. Fullarton and A. Putman, The high-dimensional cohomology of the moduli space of curves with level structures, J. Eur. Math. Soc. (JEMS) 22 (2020), no. 4, 1261-1287. arXiv:1610.03768 · Zbl 1453.14083 |
| [63] | S. Galatius, Lectures on the Madsen-Weiss theorem, in Moduli spaces of Riemann surfaces, 139-167, IAS/Park City Math. Ser., 20, Amer. Math. Soc., Providence, RI. · Zbl 1281.14023 |
| [64] | R. M. Hain, Torelli groups and geometry of moduli spaces of curves, in Current topics in complex algebraic geometry (Berkeley, CA, 1992/93), 97-143, Math. Sci. Res. Inst. Publ., 28, Cambridge Univ. Press, Cambridge. arXiv:alg-geom/9403015 · Zbl 0868.14006 |
| [65] | J. L. Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. (2) 121 (1985), no. 2, 215-249. · Zbl 0579.57005 |
| [66] | J. L. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986), no. 1, 157-176. · Zbl 0592.57009 |
| [67] | A. Hatcher, A short exposition of the Madsen-Weiss theorem, preprint. arXiv:1103.5223 |
| [68] | D. Johnson, The structure of the Torelli group. III. The abelianization of T , Topology 24 (1985), no. 2, 127-144. · Zbl 0571.57010 |
| [69] | E. Looijenga, Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map, J. Algebraic Geom. 5 (1996), no. 1, 135-150. arXiv:alg-geom/9401005 · Zbl 0860.57010 |
| [70] | H. Maazen, Homology Stability for the General Linear Group, thesis, University of Utrecht, 1979. |
| [71] | I. Madsen and M. Weiss, The stable moduli space of Riemann surfaces: Mumford’s conjec-ture, Ann. of Math. (2) 165 (2007), no. 3, 843-941. arXiv:math/0212321 · Zbl 1156.14021 |
| [72] | J. L. Mennicke, Finite factor groups of the unimodular group, Ann. of Math. (2) 81 (1965), 31-37. · Zbl 0135.06504 |
| [73] | S. Morita, T. Sakasai and M. Suzuki, Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra, Duke Math. J. 162 (2013), no. 5, 965-1002. arXiv:1107.3686 · Zbl 1308.17021 |
| [74] | B. Perron, Filtration de Johnson et groupe de Torelli modulo p, p premier, C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 667-670. · Zbl 1147.57020 |
| [75] | A. Putman, The second rational homology group of the moduli space of curves with level structures, Adv. Math. 229 (2012), no. 2, 1205-1234. arXiv:0809.4477 · Zbl 1250.14019 |
| [76] | A. Putman, The Picard group of the moduli space of curves with level structures, Duke Math. J. 161 (2012), no. 4, 623-674. arXiv:0908.0555 · Zbl 1241.30015 |
| [77] | A. Putman, The Johnson homomorphism and its kernel, J. Reine Angew. Math. 735 (2018), 109-141. arXiv:0904.0467 · Zbl 1456.57016 |
| [78] | A. Putman, A new approach to twisted homological stability, with applications to congru-ence subgroups, preprint. arXiv:2109.14015 |
| [79] | M. Sato, The abelianization of the level d mapping class group, J. Topol. 3 (2010), no. 4, 847-882. arXiv:0804.4789 · Zbl 1209.57012 |
| [80] | N. Wahl, The Mumford conjecture, Madsen-Weiss and homological stability for mapping class groups of surfaces, in Moduli spaces of Riemann surfaces, 109-138, IAS/Park City Math. Ser., 20, Amer. Math. Soc., Providence, RI. References · Zbl 1281.14022 |
| [81] | Selman Akbulut and Daniel Ruberman. Absolutely exotic compact 4-manifolds. Comment. Math. Helv., 91(1):1-19, 2016. · Zbl 1339.57003 |
| [82] | Anar Akhmedov and Doug Park. Exotic smooth structures on small 4-manifolds. Invent. Math., 173(1):209-223, 2008. · Zbl 1144.57026 |
| [83] | Anar Akhmedov and Doug Park. Exotic smooth structures on small 4-manifolds with odd signatures. Invent. Math., 181(3):577-603, 2010. · Zbl 1206.57029 |
| [84] | Steven Boyer. Realization of simply-connected 4-manifolds with a given boundary. Com-ment. Math. Helv., 68(1):20-47, 1993. · Zbl 0790.57009 |
| [85] | Anthony Conway. Homotopy ribbon discs with a fixed group. 2022. https://arxiv.org/abs/2201.04465 . |
| [86] | Anthony Conway, Lisa Piccirillo, and Mark Powell. 4-manifolds with boundary and funda-mental group Z, 2022. |
| [87] | Anthony Conway and Mark Powell. Embedded surfaces with infinite cyclic knot group. 2020. https://arxiv.org/abs/2009.13461 . · Zbl 1516.57034 |
| [88] | John B. Etnyre, Hyunki Min, and Anubhav Mukherjee. On 3-manifolds that are boundaries of exotic 4-manifolds, 2019. https://arxiv.org/abs/1901.07964 . · Zbl 1497.57030 |
| [89] | Ronald Fintushel and Ronald J. Stern. Surfaces in 4-manifolds. Math. Res. Lett., 4(6):907-914, 1997. · Zbl 0894.57014 |
| [90] | Michael H. Freedman. The disk theorem for four-dimensional manifolds. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), pages 647-663, Warsaw, 1984. PWN. · Zbl 0577.57003 |
| [91] | Michael H. Freedman and Frank Quinn. Topology of 4-manifolds, volume 39 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1990. · Zbl 0705.57001 |
| [92] | Michael Hartley Freedman. The topology of four-dimensional manifolds. J. Differential Ge-ometry, 17(3):357-453, 1982. · Zbl 0528.57011 |
| [93] | Ian Hambleton and Matthias Kreck. On the classification of topological 4-manifolds with finite fundamental group. Math. Ann., 280(1):85-104, 1988. · Zbl 0616.57009 |
| [94] | Ian Hambleton, Matthias Kreck, and Peter Teichner. Topological 4-manifolds with geomet-rically two-dimensional fundamental groups. J. Topol. Anal., 1(2):123-151, 2009. · Zbl 1179.57034 |
| [95] | Kyle Hayden. Exotic ribbon disks and symplectic surfaces. 2020. https://arxiv.org/abs/2003.13681. |
| [96] | Neil R. Hoffman and Nathan S. Sunukjian. Null-homologous exotic surfaces in 4-manifolds. Algebr. Geom. Topol., 20(5):2677-2685, 2020. · Zbl 1464.57031 |
| [97] | Jongil Park. The geography of symplectic 4-manifolds with an arbitrary fundamental group. Proc. Amer. Math. Soc., 135(7):2301-2307, 2007. · Zbl 1116.57023 |
| [98] | Richard Stong and Zhenghan Wang. Self-homeomorphisms of 4-manifolds with fundamental group Z. Topology Appl., 106(1):49-56, 2000. · Zbl 0974.57014 |
| [99] | Rafael Torres. Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds, 2020. |
| [100] | Kupers, A. and Randal-Williams, O., On the Torelli Lie algebra, arXiv preprint (2021), https://arxiv.org/abs/2106.16010. |
| [101] | Felder, M., Naef, F. and Willwacher, T., Stable cohomology of graph complexes, arXiv preprint (2021), https://arxiv.org/abs/2106.12826. |
| [102] | Kupers, A. and Randal-Williams, O., On diffeomorphisms of even-dimensional discs, arXiv preprint (2020), https://arxiv.org/abs/2007.13884. References |
| [103] | Matthew Ando. Isogenies of formal group laws and power operations in the cohomol-ogy theories En. Duke Math. J., 79(2):423-485, 1995. · Zbl 0862.55004 |
| [104] | William Balderrama. Algebraic theories of power operations. 2021. arXiv:2108.06802. |
| [105] | Andrew Baker and Birgit Richter. Galois extensions of Lubin-Tate spectra. Homol-ogy, Homotopy and Applications, 10(3):27-43, 2008. · Zbl 1175.55007 |
| [106] | Dustin Clausen, Akhil Mathew, Niko Naumann, and Justin Noel. Descent and vanish-ing in chromatic algebraic K-theory via group actions. Nov 2020. arXiv:2011.08233. · Zbl 1453.18011 |
| [107] | P. G. Goerss and M. J. Hopkins. Moduli spaces of commutative ring spectra. In Structured ring spectra, volume 315 of London Math. Soc. Lecture Note Ser., pages 151-200. Cambridge Univ. Press, Cambridge, 2004. · Zbl 1086.55006 |
| [108] | Jeremy Hahn. On the Bousfield classes of H∞-ring spectra. 2016. arXiv:1612.04386. |
| [109] | Michael J Hopkins and Tyler Lawson. Strictly commutative complex orientation theory. Mathematische Zeitschrift, 290(1):83-101, 2018. · Zbl 1417.55012 |
| [110] | Jeremy Hahn and Allen Yuan. Exotic multiplications on periodic complex bordism. Journal of Topology, 13(4):1839-1852, 2020. · Zbl 1461.55007 |
| [111] | Markus Land, Akhil Mathew, Lennart Meier, and Georg Tamme. Purity in chromat-ically localized algebraic K-theory. 2020. arXiv:2001.10425. |
| [112] | Jacob Lurie. Elliptic Cohomology II: Orientations. 2018. Available online. |
| [113] | Jan-David Möllers. K(1)-local complex E∞-orientations. Thesis (Ph.D.)-Ruhr-Universität Bochum, 2010. |
| [114] | Barry John Walker. Multiplicative orientations of K-Theory and p-adic analysis. University of Illinois at Urbana-Champaign, 2008. |
| [115] | Allen Yuan. Examples of chromatic redshift in algebraic K-theory. 2021. arXiv:2111.10837. |
| [116] | Yifei Zhu. Norm coherence for descent of level structures on formal deformations. Journal of Pure and Applied Algebra, 224(10):106382, 2020. References · Zbl 07195678 |
| [117] | P. Caprace and M. Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal., 21(4) (2011), 851-891. · Zbl 1266.20054 |
| [118] | A. Genevois, Contracting isometries of CAT(0) cube complexes and acylindrical hyperbol-icity of diagram groups Algebr. Geom. Topol. 20(1) (2020), 49-134. · Zbl 1481.20151 |
| [119] | A. Genevois, Hyperbolicities in CAT(0) cube complexes, Enseign. Math., 65(1-2) (2020), 33-100. · Zbl 1472.20090 |
| [120] | M. Hagen, Weak hyperbolicity of cube complexes and quasi-arboreal groups, J. Topol., 7(2) (2014), 385-418. · Zbl 1348.20044 |
| [121] | N. Ivanov, Automorphisms of complexes of curves and of Teichmüller space, Progress in knot theory and related topics, volume 56 of Travaux en Cours (1997), 113-120. · Zbl 0941.30027 |
| [122] | H. Masur and Y. Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math., 138(1) (1999), 103-149. · Zbl 0941.32012 |
| [123] | H. Petyt, D. Spriano and A. Zalloum, Hyperbolic models for CAT(0) sapaces, arXiv:2207.14127. References |
| [124] | K. Hayden, S. Kim, M. Miller, JH. Park, I. Sundberg, Seifert surfaces in the 4-ball, arXiv [math.GT] 2205.15283, 2022. |
| [125] | C. Livingston, Surfaces bounding the unlink, Michigan Mathematical Journal 29 (1982):3, 289-298. · Zbl 0522.57004 |
| [126] | H.C. Lyon, Simple knots without unique minimal surfaces, Proceedings of the American Mathematical Society 43 (1974), 449-454. · Zbl 0247.55003 |
| [127] | Hyman Bass. Unitary algebraic K-theory. In Algebraic K-theory, III: Hermitian K-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 57-265. Lecture Notes in Math., Vol. 343, 1973. · Zbl 0299.18005 |
| [128] | Steven Boyer. Realization of simply-connected 4-manifolds with a given boundary. Comment. Math. Helv., 68(1):20-47, 1993. · Zbl 0790.57009 |
| [129] | Inanç Baykur and Nathan Sunukjian. Knotted surfaces in 4-manifolds and stabiliza-tions. J. Topol., 9(1):215-231, 2016. · Zbl 1339.57028 |
| [130] | Anthony Conway. Homotopy ribbon discs with a fixed group. 2022. https://arxiv.org/pdf/2201.04465. |
| [131] | Anthony Conway and Mark Powell. Embedded surfaces with infinite cyclic knot group. Geom. Topol., 2020. · Zbl 1516.57034 |
| [132] | Anthony Conway and Mark Powell. Characterisation of homotopy ribbon discs. Adv. Math., 391:Paper No. 107960, 29, 2021. · Zbl 1476.57007 |
| [133] | Anthony Conway, Lisa Piccirillo, and Mark Powell. 4-manifolds with boundary and fundamental group Z. 2022. https://arxiv.org/pdf/2205.12774. |
| [134] | Peter Feller and Lukas Lewark. Balanced algebraic unknotting, linking forms, and surfaces in three-and four-space. 2019. https://arxiv.org/pdf/1905.08305. |
| [135] | + 21] Peter Feller, Allison N. Miller, Matthias Nagel, Patrick Orson, Mark Powell, and Arunima Ray. Embedding spheres in knot traces. Compos. Math., 157(10):2242-2279, 2021. · Zbl 1486.57026 |
| [136] | Michael Hartley Freedman. The topology of four-dimensional manifolds. J. Differen-tial Geometry, 17(3):357-453, 1982. · Zbl 0528.57011 |
| [137] | Stefan Friedl and Peter Teichner. New topologically slice knots. Geom. Topol., 9:2129-2158, 2005. · Zbl 1120.57004 |
| [138] | Daniel Kasprowski, Mark Powell, Arunima Ray, and Peter Teichner. Embedding surfaces in 4-manifolds. 2022. https://arxiv.org/pdf/2201.03961. · Zbl 1516.57035 |
| [139] | Ronnie Lee and Dariusz M. Wilczyński. Locally flat 2-spheres in simply connected 4-manifolds. Comment. Math. Helv., 65(3):388-412, 1990. · Zbl 0723.57015 |
| [140] | Ronnie Lee and Dariusz M. Wilczyński. Representing homology classes by locally flat 2-spheres. K-Theory, 7(4):333-367, 1993. · Zbl 0805.57014 |
| [141] | Ronnie Lee and Dariusz M. Wilczyński. Representing homology classes by locally flat surfaces of minimum genus. Amer. J. Math., 119(5):1119-1137, 1997. · Zbl 0886.57027 |
| [142] | Ronnie Lee and Dariusz M. Wilczyński. Genus inequalities and four-dimensional surgery. Topology, 39(2):311-330, 2000. · Zbl 0938.57026 |
| [143] | Frank Quinn. Isotopy of 4-manifolds. J. Differential Geom., 24(3):343-372, 1986. · Zbl 0617.57007 |
| [144] | Nathan S. Sunukjian. Surfaces in 4-manifolds: concordance, isotopy, and surgery. Int. Math. Res. Not. IMRN, (17):7950-7978, 2015. References · Zbl 1326.57043 |
| [145] | Berwick-Evans, Daniel, and Arnav Tripathy. A de Rham model for complex analytic equi-variant elliptic cohomology, Advances in Mathematics 380 (2021): 107575. · Zbl 1472.14027 |
| [146] | Ginzburg, Victor, Mikhail Kapranov, and Eric Vasserot. Elliptic algebras and equivariant elliptic cohomology, arXiv preprint q-alg/9505012 (1995). |
| [147] | Grojnowski, Ian. Delocalised equivariant elliptic cohomology., Elliptic Cohomology, London Math. Soc. Lecture Note Ser 342 (1994): 114-121. · Zbl 1236.55008 |
| [148] | Lurie, Jacob. A survey of elliptic cohomology, Algebraic topology. Springer, Berlin, Heidel-berg, 2009. 219-277. · Zbl 1206.55007 |
| [149] | Lurie, Jacob. Spectral algebraic geometry. Available on the author’s homepage. |
| [150] | Swan, Richard G. The Nontrivality of the Restriction Map in the Cohomology of Groups, Proceedings of the American Mathematical Society 11.6 (1960): 885-887. · Zbl 0096.25302 |
| [151] | R. H. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka Journal of Mathematics 3(2) (1966), 257-267. · Zbl 0146.45501 |
| [152] | J. Hom, S. Kang, and J. Park, Ribbon knots, cabling, and handle decompositions, arXiv preprint arXiv:2003.02832 (2020). · Zbl 1502.57005 |
| [153] | M. Khovanov, Patterns in knot cohomology, I, Experimental mathematics 12(3) (2003), 365-374. · Zbl 1073.57007 |
| [154] | P. S. Ozsváth and Z. Szabó, Holomorphic disks and knot invariants, Advances in Mathe-matics 186(1) (2004), 58-116. · Zbl 1062.57019 |
| [155] | L. Piccirillo, The Conway knot is not slice, Annals of Mathematics 191(2) (2020), 581-591. · Zbl 1471.57011 |
| [156] | J. A. Rasmussen, Floer homology and knot complements, Harvard University (2003), PhD thesis. |
| [157] | S. Basu, S. Sagave, and C. Schlichtkrull Generalized Thom spectra and their topological Hochschild homology, Journal of the Institute of Mathematics of Jussieu 19 (2020), 21-64 · Zbl 1430.19006 |
| [158] | J. Beardsley Relative Thom spectra via operadic Kan extensions, Algebraic & Geometric Topology 17 (2017), 1151-1162 · Zbl 1420.55010 |
| [159] | J. Greenlees Ausoni-Bökstedt duality for topological Hochschild homology, Journal of Pure and Applied Algebra 220 (2016), 1382-1402 · Zbl 1332.55003 |
| [160] | M. Hill Freeness and equivariant stable homotopy, Journal of Topology 15 (2022), 359-397 · Zbl 1530.55007 |
| [161] | M. Hill, M. Hopkins, and D. Ravenel, On the nonexistence of elements of Kervaire invariant one, Annals of Mathematics 184 (2016), 1-262. · Zbl 1366.55007 |
| [162] | P. Hu and I. Kriz, Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence, Topology 40 (2001), 317-399 · Zbl 0967.55010 |
| [163] | T. Goodwillie, A multiple disjunction lemma for smooth concordance embeddings, Mem. Amer. Math. Soc. 86 (1990), no. 431, viii+317 pp. · Zbl 0717.57011 |
| [164] | T. Goodwillie and J. Klein, Multiple disjunction for spaces of smooth embeddings, J. Topol. 8 (2015), no. 3, 651-674. · Zbl 1329.57029 |
| [165] | T. Goodwillie, M. Krannich, and A. Kupers, Stability for concordance embeddings, arXiv:2207.13216. |
| [166] | T. Goodwillie and M. Weiss, Embeddings from the point of view of immersion theory. II, Geom. Topol. 3 (1999), 103-118. · Zbl 0927.57028 |
| [167] | A. Hatcher, Higher simple homotopy theory, Ann. of Math. (2) 102 (1975), no. 1, 101-137. · Zbl 0305.57009 |
| [168] | K. Igusa, The stability theorem for smooth pseudoisotopies, K-Theory 2 (1988), no. 1-2, vi+355. · Zbl 0691.57011 |
| [169] | M. Krannich and O. Randal-Williams, Diffeomorphisms of discs and the second Weiss de-rivative of BTop(-), arXiv:2109.03500. |
| [170] | G. Meng, The stability theorem for smooth concordance imbeddings, 1993, Thesis (Ph.D.) Brown University. |
| [171] | M. Weiss, Embeddings from the point of view of immersion theory. I, Geom. Topol. 3 (1999), 67-101. · Zbl 0927.57027 |
| [172] | M. Weiss, Orthogonal Calculus, Trans. Amer. Math. Soc. 347 (1995), no. 10, 3743-3796. Reporter: Alexis Aumonier · Zbl 0866.55020 |
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.
