Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 7, 2431–2778
Issue 6, 2043–2429
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

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
Cables of the figure-eight knot via real Frøyshov invariants

Sungkyung Kang, JungHwan Park and Masaki Taniguchi

Geometry & Topology 30 (2026) 781–833
Bibliography
1 T Abe, K Tagami, Fibered knots with the same 0-surgery and the slice-ribbon conjecture, Math. Res. Lett. 23 (2016) 303 MR3512887
2 P Aceto, N A Castro, M Miller, J Park, A Stipsicz, Slice obstructions from genus bounds in definite 4-manifolds, preprint (2023) arXiv:2303.10587
3 J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR764596
4 A Alfieri, S Kang, A I Stipsicz, Connected Floer homology of covering involutions, Math. Ann. 377 (2020) 1427 MR4126897
5 K L Baker, A note on the concordance of fibered knots, J. Topol. 9 (2016) 1 MR3465837
6 J A Baldwin, S Sivek, Framed instanton homology and concordance, J. Topol. 14 (2021) 1113 MR4332488
7 J A Baldwin, S Sivek, Framed instanton homology and concordance, II, preprint (2022) arXiv:2206.11531
8 W Ballinger, Configurations of spheres in #nP2, preprint (2022) arXiv:2209.12851
9 D Baraglia, Knot concordance invariants from Seiberg–Witten theory and slice genus bounds in 4-manifolds, Internat. J. Math. 35 (2024) 2450032 MR4793229
10 D Baraglia, P Hekmati, Equivariant Seiberg–Witten–Floer cohomology, Algebr. Geom. Topol. 24 (2024) 493 MR4721374
11 D Baraglia, P Hekmati, New invariants of involutions from Seiberg–Witten Floer theory, preprint (2024) arXiv:2403.00203
12 G Carlsson, Equivariant stable homotopy and Sullivan’s conjecture, Invent. Math. 103 (1991) 497 MR1091616
13 A J Casson, C M Gordon, A loop theorem for duality spaces and fibred ribbon knots, Invent. Math. 74 (1983) 119 MR722728
14 J C Cha, The structure of the rational concordance group of knots, 885, Amer. Math. Soc. (2007) MR2343079
15 J C Cha, C Livingston, D Ruberman, Algebraic and Heegaard–Floer invariants of knots with slice Bing doubles, Math. Proc. Cambridge Philos. Soc. 144 (2008) 403 MR2405897
16 A Conway, M H Kim, W Politarczyk, Nonslice linear combinations of iterated torus knots, Algebr. Geom. Topol. 23 (2023) 765 MR4587316
17 A Daemi, C Scaduto, Chern–Simons functional, singular instantons, and the four-dimensional clasp number, J. Eur. Math. Soc. 26 (2024) 2127 MR4742808
18 A Daemi, C Scaduto, Equivariant aspects of singular instanton Floer homology, Geom. Topol. 28 (2024) 4057 MR4845451
19 A Daemi, H Imori, K Sato, C Scaduto, M Taniguchi, Instantons, special cycles and knot concordance, Geom. Topol. 29 (2025) 4189 MR5000788
20 I Dai, C Manolescu, Involutive Heegaard Floer homology and plumbed three-manifolds, J. Inst. Math. Jussieu 18 (2019) 1115 MR4021102
21 I Dai, H Sasahira, M Stoffregen, Lattice homology and Seiberg–Witten–Floer spectra, preprint (2023) arXiv:2309.01253
22 I Dai, S Kang, A Mallick, J Park, M Stoffregen, The (2,1)-cable of the figure-eight knot is not smoothly slice, Invent. Math. 238 (2024) 371 MR4809438
23 T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
24 W Dwyer, H Miller, J Neisendorfer, Fibrewise completion and unstable Adams spectral sequences, Israel J. Math. 66 (1989) 160 MR1017160
25 P Feller, J Park, A note on the four-dimensional clasp number of knots, Math. Proc. Cambridge Philos. Soc. 173 (2022) 213 MR4438338
26 R H Fox, Some problems in knot theory, from: "Topology of 3-manifolds and related topics" (editor M K Fort Jr), Prentice-Hall (1961) 168 MR140100
27 S Ghosh, Z Li, C M M Wong, On the tau invariants in instanton and monopole Floer theories, J. Topol. 17 (2024) MR4821358
28 C M Gordon, R A Litherland, K Murasugi, Signatures of covering links, Canadian J. Math. 33 (1981) 381 MR617628
29 J E Greene, L-space surgeries, genus bounds, and the cabling conjecture, J. Differential Geom. 100 (2015) 491 MR3352796
30 M Hedden, P Kirk, C Livingston, Non-slice linear combinations of algebraic knots, J. Eur. Math. Soc. 14 (2012) 1181 MR2928848
31 J Hom, A survey on Heegaard Floer homology and concordance, J. Knot Theory Ramifications 26 (2017) 1740015 MR3604497
32 J Hom, S Kang, J Park, M Stoffregen, Linear independence of rationally slice knots, Geom. Topol. 26 (2022) 3143 MR4540903
33 N Iida, M Taniguchi, Monopoles and transverse knots, preprint (2024) arXiv:2403.15763
34 A Juhász, I Zemke, New Heegaard Floer slice genus and clasp number bounds, preprint (2020) arXiv:2007.07106
35 Ç Karakurt, O Şavk, Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology, Acta Math. Hungar. 168 (2022) 454 MR4527512
36 Y Kato, Nonsmoothable actions of 2 × 2 on spin four-manifolds, Topology Appl. 307 (2022) 107868 MR4365044
37 A Kawauchi, The (1,2)-cable of the figure eight knot is rationally slice, unpublished work (1980)
38 A Kawauchi, On links not cobordant to split links, Topology 19 (1980) 321 MR584558
39 A Kawauchi, Rational-slice knots via strongly negative-amphicheiral knots, Commun. Math. Res. 25 (2009) 177 MR2554510
40 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
41 M H Kim, Z Wu, On rational sliceness of Miyazaki’s fibered, -amphicheiral knots, Bull. Lond. Math. Soc. 50 (2018) 462 MR3829733
42 H Konno, A Mallick, M Taniguchi, From diffeomorphisms to exotic phenomena in small 4-manifolds, preprint (2023) arXiv:2304.05997
43 H Konno, J Miyazawa, M Taniguchi, Involutions, links, and Floer cohomologies, J. Topol. 17 (2024) MR4821360
44 H Konno, J Miyazawa, M Taniguchi, Involutions, knots, and Floer K-theory, Compos. Math. 161 (2025) 2852 MR5002153
45 P B Kronheimer, T S Mrowka, Gauge theory and Rasmussen’s invariant, J. Topol. 6 (2013) 659 MR3100886
46 P B Kronheimer, T S Mrowka, Instantons and some concordance invariants of knots, J. Lond. Math. Soc. (2) 104 (2021) 541 MR4311103
47 J Lannes, Sur les espaces fonctionnels dont la source est le classifiant d’un p-groupe abélien élémentaire, Inst. Hautes Études Sci. Publ. Math. (1992) 135 MR1179079
48 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR246314
49 J Li, Monopole Floer homology and real structures, preprint (2022) arXiv:2211.10768
50 J Li, Real monopole Floer homology and skein exact triangles, preprint (2023) arXiv:2304.01742
51 W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
52 T Lidman, C Manolescu, The equivalence of two Seiberg–Witten Floer homologies, 399 (2018) MR3818611
53 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 327 MR780587
54 C Livingston, Signed clasp numbers and four-genus bounds, preprint (2022) arXiv:2206.10432
55 C Manolescu, Seiberg–Witten–Floer stable homotopy type of three-manifolds with b1 = 0, Geom. Topol. 7 (2003) 889 MR2026550
56 C Manolescu, A gluing theorem for the relative Bauer–Furuta invariants, J. Differential Geom. 76 (2007) 117 MR2312050
57 C Manolescu, M Marengon, S Sarkar, M Willis, A generalization of Rasmussen’s invariant, with applications to surfaces in some four-manifolds, Duke Math. J. 172 (2023) 231 MR4541332
58 A N Miller, Amphichiral knots with large 4-genus, Bull. Lond. Math. Soc. 54 (2022) 624 MR4453695
59 K Miyazaki, Nonsimple, ribbon fibered knots, Trans. Amer. Math. Soc. 341 (1994) 1 MR1176509
60 J Miyazawa, A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P2-knots, preprint (2023) arXiv:2312.02041
61 I Montague, Seiberg–Witten Floer K-theory and cyclic group actions on spin four-manifolds with boundary, preprint (2022) arXiv:2210.08565
62 L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
63 T Mrowka, P Ozsváth, B Yu, Seiberg–Witten monopoles on Seifert fibered spaces, Comm. Anal. Geom. 5 (1997) 685 MR1611061
64 N Nakamura, Pin(2)-monopole equations and intersection forms with local coefficients of four-manifolds, Math. Ann. 357 (2013) 915 MR3118618
65 N Nakamura, Pin(2)-monopole invariants, J. Differential Geom. 101 (2015) 507 MR3415770
66 A Némethi, On the Ozsváth–Szabó invariant of negative definite plumbed 3-manifolds, Geom. Topol. 9 (2005) 991 MR2140997
67 A Némethi, Lattice cohomology of normal surface singularities, Publ. Res. Inst. Math. Sci. 44 (2008) 507 MR2426357
68 W D Neumann, An invariant of plumbed homology spheres, from: "Topology symposium" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 125 MR585657
69 Y Ni, X Zhang, Characterizing slopes for torus knots, Algebr. Geom. Topol. 14 (2014) 1249 MR3190593
70 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
71 P Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003) 185 MR1988284
72 S P Plotnick, Fibered knots in S4 : twisting, spinning, rolling, surgery, and branching, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 437 MR780592
73 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) arXiv:math/0306378 MR2704683
74 J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
75 L Rudolph, How independent are the knot-cobordism classes of links of plane curve singularities?, Notices Amer. Math. Soc 23 (1976) 410
76 S J Schiffman, A mod p Whitehead theorem, Proc. Amer. Math. Soc. 82 (1981) 139 MR603617
77 T Shibuya, Some relations among various numerical invariants for links, Osaka Math. J. 11 (1974) 313 MR353295
78 L Siebenmann, On vanishing of the Rohlin invariant and nonfinitely amphicheiral homology 3-spheres, from: "Topology symposium" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 172 MR585660
79 G Tian, S Wang, Orientability and real Seiberg–Witten invariants, Internat. J. Math. 20 (2009) 573 MR2526308
80 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR248854