Geometry & Topology Volume 29, issue 8 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Instantons, special cycles and knot concordance

Aliakbar Daemi, Hayato Imori, Kouki Sato, Christopher Scaduto and Masaki Taniguchi

Geometry & Topology 29 (2025) 4189–4298

DOI: 10.2140/gt.2025.29.4189

Bibliography

1	J A Baldwin, S Sivek, Framed instanton homology and concordance, J. Topol. 14 (2021) 1113 MR4332488
2	J A Baldwin, S Sivek, Framed instanton homology and concordance, II, preprint (2022) arXiv:2206.11531
3	D Baraglia, Knot concordance invariants from Seiberg–Witten theory and slice genus bounds in 4-manifolds, Internat. J. Math. 35 (2024) MR4793229
4	O Collin, N Saveliev, A geometric proof of the Fintushel–Stern formula, Adv. Math. 147 (1999) 304 MR1734525
5	A Daemi, Chern–Simons functional and the homology cobordism group, Duke Math. J. 169 (2020) 2827 MR4158669
6	A Daemi, C Scaduto, Chern–Simons functional, singular instantons, and the four-dimensional clasp number, J. Eur. Math. Soc. 26 (2024) 2127 MR4742808
7	A Daemi, C Scaduto, Equivariant aspects of singular instanton Floer homology, Geom. Topol. 28 (2024) 4057 MR4845451
8	M Echeverria, A generalization of the Tristram–Levine knot signatures as a singular Furuta–Ohta invariant for tori, preprint (2019) arXiv:1908.11359
9	R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. 61 (1990) 109 MR1051101
10	R Fintushel, R J Stern, Integer graded instanton homology groups for homology three-spheres, Topology 31 (1992) 589 MR1174261
11	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR679066
12	K A Frøyshov, Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002) 525 MR1910040
13	M Furuta, Homology cobordism group of homology 3-spheres, Invent. Math. 100 (1990) 339 MR1047138
14	S Ghosh, Z Li, C M M Wong, On the tau invariants in instanton and monopole Floer theories, J. Topol. 17 (2024) MR4821358
15	S Gong, On the Kronheimer–Mrowka concordance invariant, J. Topol. 14 (2021) 1 MR4186131
16	M Hedden, P Kirk, Instantons, concordance, and Whitehead doubling, J. Differential Geom. 91 (2012) 281 MR2971290
17	M Hedden, J Pinzón-Caicedo, Satellites of infinite rank in the smooth concordance group, Invent. Math. 225 (2021) 131 MR4270665
18	C M Herald, Existence of irreducible representations for knot complements with nonconstant equivariant signature, Math. Ann. 309 (1997) 21 MR1467643
19	C M Herald, Flat connections, the Alexander invariant, and Casson’s invariant, Comm. Anal. Geom. 5 (1997) 93 MR1456309
20	M Heusener, J Kroll, Deforming abelian SU(2)-representations of knot groups, Comment. Math. Helv. 73 (1998) 480 MR1633375
21	J Hom, Bordered Heegaard Floer homology and the tau-invariant of cable knots, J. Topol. 7 (2014) 287 MR3217622
22	J Hom, Z Wu, Four-ball genus bounds and a refinement of the Ozsváth–Szabó tau invariant, J. Symplectic Geom. 14 (2016) 305 MR3523259
23	H Imori, Instanton knot invariants with rational holonomy parameters and an application for torus knot groups, Algebr. Geom. Topol. 24 (2024) 5045 MR4845979
24	P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, I, Topology 32 (1993) 773 MR1241873
25	P B Kronheimer, T S Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. 113 (2011) 97 MR2805599
26	P B Kronheimer, T S Mrowka, Knot homology groups from instantons, J. Topol. 4 (2011) 835 MR2860345
27	P B Kronheimer, T S Mrowka, Gauge theory and Rasmussen’s invariant, J. Topol. 6 (2013) 659 MR3100886
28	P B Kronheimer, T S Mrowka, Instantons and Bar-Natan homology, Compos. Math. 157 (2021) 484 MR4236193
29	P B Kronheimer, T S Mrowka, Instantons and some concordance invariants of knots, J. Lond. Math. Soc. 104 (2021) 541 MR4311103
30	L Lewark, Rasmussen’s spectral sequences and the 𝔰𝔩_N-concordance invariants, Adv. Math. 260 (2014) 59 MR3209349
31	Z Li, Knot homologies in monopole and instanton theories via sutures, J. Symplectic Geom. 19 (2021) 1339 MR4450625
32	R A Litherland, Signatures of iterated torus knots, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 71 MR547456
33	C Livingston, Seifert forms and concordance, Geom. Topol. 6 (2002) 403 MR1928840
34	C Livingston, Computations of the Ozsváth–Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735 MR2057779
35	C Livingston, A H Moore, KnotInfo: table of knot invariants, (2004)
36	C Manolescu, Homology cobordism and triangulations, from: "Proceedings of the International Congress of Mathematicians" (editors B Sirakov, P Ney de Souza, M Viana), World Sci. Publ. (2018) 1175 MR3966804
37	J Milnor, Singular points of complex hypersurfaces, 61, Princeton Univ. Press (1968) MR239612
38	Y Nozaki, K Sato, M Taniguchi, Filtered instanton Floer homology and the homology cobordism group, J. Eur. Math. Soc. 26 (2024) 4699 MR4780492
39	P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
40	P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
41	P S Ozsváth, Z Szabó, Knot Floer homology and rational surgeries, Algebr. Geom. Topol. 11 (2011) 1 MR2764036
42	K Park, On independence of iterated Whitehead doubles in the knot concordance group, J. Knot Theory Ramifications 27 (2018) MR3749499
43	J Pinzón-Caicedo, Independence of iterated Whitehead doubles, Proc. Amer. Math. Soc. 147 (2019) 1313 MR3896076
44	J H Przytycki, Positive knots have negative signature, Bull. Polish Acad. Sci. Math. 37 (1989) 559 MR1101920
45	J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
46	D Ruberman, On smoothly superslice knots, New York J. Math. 22 (2016) 711 MR3548119
47	L Rudolph, Constructions of quasipositive knots and links, III : A characterization of quasipositive Seifert surfaces, Topology 31 (1992) 231 MR1167166
48	L Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. 29 (1993) 51 MR1193540
49	L Rudolph, Quasipositive plumbing (constructions of quasipositive knots and links, V), Proc. Amer. Math. Soc. 126 (1998) 257 MR1452826
50	T Sano, A description of Rasmussen’s invariant from the divisibility of Lee’s canonical class, J. Knot Theory Ramifications 29 (2020) MR4125174
51	K Sato, Topologically slice knots that are not smoothly slice in any definite 4-manifold, Algebr. Geom. Topol. 18 (2018) 827 MR3773740
52	K Sato, The ν⁺-equivalence classes of genus one knots, Selecta Math. 29 (2023) MR4629937
53	M Stoffregen, Pin(2)-equivariant Seiberg–Witten Floer homology of Seifert fibrations, Compos. Math. 156 (2020) 199 MR4044465
54	C H Taubes, Gauge theory on asymptotically periodic 4-manifolds, J. Differential Geom. 25 (1987) 363 MR882829
55	K Yasui, Corks, exotic 4-manifolds and knot concordance, preprint (2015) arXiv:1505.02551