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Instanton knot invariants with rational holonomy parameters and an application for torus knot groups

Hayato Imori

Algebraic & Geometric Topology 24 (2024) 5045–5122
Bibliography
1 P J Braam, S K Donaldson, Floer’s work on instanton homology, knots and surgery, from: "The Floer memorial volume", Progr. Math. 133, Birkhäuser (1995) 195 MR1362829
2 O Collin, N Saveliev, A geometric proof of the Fintushel–Stern formula, Adv. Math. 147 (1999) 304 MR1734525
3 O Collin, B Steer, Instanton Floer homology for knots via 3–orbifolds, J. Differential Geom. 51 (1999) 149 MR1703606
4 L Culler, A Daemi, Y Xie, Surgery, polygons and SU(N)–Floer homology, J. Topol. 13 (2020) 576 MR4092776
5 A Daemi, Chern–Simons functional and the homology cobordism group, Duke Math. J. 169 (2020) 2827 MR4158669
6 A Daemi, H Imori, K Sato, C Scaduto, M Taniguchi, Instantons, special cycles, and knot concordance, (2022) arXiv:2209.05400
7 A Daemi, T Lidman, D S Vela-Vick, C M M Wong, Ribbon homology cobordisms, Adv. Math. 408 (2022) 108580 MR4467148
8 A Daemi, C Scaduto, Chern–Simons functional, singular instantons, and the four-dimensional clasp number, J. Eur. Math. Soc. 26 (2024) 2127 MR4742808
9 A Daemi, C Scaduto, Equivariant aspects of singular instanton Floer homology, Geom. Topol. 28 (2024) 4057
10 S K Donaldson, Floer homology groups in Yang–Mills theory, 147, Cambridge Univ. Press (2002) MR1883043
11 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Univ. Press (1990) MR1079726
12 M Echeverria, A generalization of the Tristram–Levine knot signatures as a singular Furuta–Ohta invariant for tori, preprint (2019) arXiv:1908.11359
13 R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. Lond. Math. Soc. 61 (1990) 109 MR1051101
14 A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
15 A Floer, Instanton homology, surgery, and knots, from: "Geometry of low-dimensional manifolds, I", Lond. Math. Soc. Lect. Note Ser. 150, Cambridge Univ. Press (1990) 97 MR1171893
16 R H Fox, Some problems in knot theory, from: "Topology of 3–manifolds and related topics", Prentice-Hall (1961) 168 MR140100
17 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
18 K A Frøyshov, Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002) 525 MR1910040
19 K A Frøyshov, An inequality for the h–invariant in instanton Floer theory, Topology 43 (2004) 407 MR2052970
20 K Fukaya, Floer homology of connected sum of homology 3–spheres, Topology 35 (1996) 89 MR1367277
21 C M Gordon, Ribbon concordance of knots in the 3–sphere, Math. Ann. 257 (1981) 157 MR634459
22 C M Herald, Legendrian cobordism and Chern–Simons theory on 3–manifolds with boundary, Comm. Anal. Geom. 2 (1994) 337 MR1305710
23 C M Herald, Flat connections, the Alexander invariant, and Casson’s invariant, Comm. Anal. Geom. 5 (1997) 93 MR1456309
24 E P Klassen, Representations of knot groups in SU(2), Trans. Amer. Math. Soc. 326 (1991) 795 MR1008696
25 P B Kronheimer, An obstruction to removing intersection points in immersed surfaces, Topology 36 (1997) 931 MR1432428
26 P B Kronheimer, Four-manifold invariants from higher-rank bundles, J. Differential Geom. 70 (2005) 59 MR2192061
27 P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, I, Topology 32 (1993) 773 MR1241873
28 P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, II, Topology 34 (1995) 37 MR1308489
29 P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU(2), Math. Res. Lett. 11 (2004) 741 MR2106239
30 P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) MR2388043
31 P Kronheimer, T Mrowka, Knots, sutures, and excision, J. Differential Geom. 84 (2010) 301 MR2652464
32 P B Kronheimer, T S Mrowka, Knot homology groups from instantons, J. Topol. 4 (2011) 835 MR2860345
33 X S Lin, A knot invariant via representation spaces, J. Differential Geom. 35 (1992) 337 MR1158339
34 R A Litherland, Signatures of iterated torus knots, from: "Topology of low-dimensional manifolds", Lecture Notes in Math. 722, Springer (1979) 71 MR547456
35 Y Nozaki, K Sato, M Taniguchi, Filtered instanton Floer homology and the homology cobordism group, J. Eur. Math. Soc. 26 (2024) 4699 MR4780492
36 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
37 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
38 C D Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Proc. Nat. Acad. Sci. U.S.A. 43 (1957) 169 MR82671
39 P Poudel, N Saveliev, Link homology and equivariant gauge theory, Algebr. Geom. Topol. 17 (2017) 2635 MR3704238
40 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) MR2704683
41 O Y Viro, Branched coverings of manifolds with boundary and link invariants, I, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 1241 MR370605