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

Volume 30
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