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

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Thin knots and the cabling conjecture

Robert DeYeso III

Algebraic & Geometric Topology 25 (2025) 4547–4583
Bibliography
1 H Bodish, R DeYeso III, Obstructing reducible surgeries: slice genus and thickness bounds, preprint (2022) arXiv:2209.01672
2 S Boyer, Dehn surgery on knots, from: "Handbook of geometric topology", North-Holland (2002) 165 MR1886670
3 S Boyer, X Zhang, Reducing Dehn filling and toroidal Dehn filling, Topology Appl. 68 (1996) 285 MR1377050
4 S Boyer, X Zhang, On Culler–Shalen seminorms and Dehn filling, Ann. of Math. 148 (1998) 737 MR1670053
5 S Dey, On Heegaard Floer theoretic properties of knots, PhD thesis, State University of New York at Buffalo (2021) MR4336881
6 M Eudave Muñoz, Band sums of links which yield composite links: the cabling conjecture for strongly invertible knots, Trans. Amer. Math. Soc. 330 (1992) 463 MR1112545
7 D Gabai, Foliations and the topology of 3-manifolds, III, J. Differential Geom. 26 (1987) 479 MR910018
8 F González-Acuña, H Short, Knot surgery and primeness, Math. Proc. Cambridge Philos. Soc. 99 (1986) 89 MR809502
9 C M Gordon, J Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987) 97 MR886439
10 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
11 J E Greene, L-space surgeries, genus bounds, and the cabling conjecture, J. Differential Geom. 100 (2015) 491 MR3352796
12 C M Grove, A combinatorial approach to the cabling conjecture, PhD thesis, The University of Iowa (2016) MR3564041
13 J Hanselman, Heegaard Floer homology and cosmetic surgeries in S3, J. Eur. Math. Soc. (JEMS) 25 (2023) 1627 MR4592856
14 J Hanselman, Knot Floer homology as immersed curves, preprint (2023) arXiv:2305.16271
15 J Hanselman, J Rasmussen, L Watson, Heegaard Floer homology for manifolds with torus boundary : properties and examples, Proc. Lond. Math. Soc. 125 (2022) 879 MR4500201
16 J Hanselman, J Rasmussen, L Watson, Bordered Floer homology for manifolds with torus boundary via immersed curves, J. Amer. Math. Soc. 37 (2024) 391 MR4695506
17 J Hanselman, L Watson, A calculus for bordered Floer homology, Geom. Topol. 27 (2023) 823 MR4599308
18 C Hayashi, K Shimokawa, Symmetric knots satisfy the cabling conjecture, Math. Proc. Cambridge Philos. Soc. 123 (1998) 501 MR1607989
19 J Hom, A survey on Heegaard Floer homology and concordance, J. Knot Theory Ramifications 26 (2017) 1740015 MR3604497
20 J Hom, T Lidman, N Zufelt, Reducible surgeries and Heegaard Floer homology, Math. Res. Lett. 22 (2015) 763 MR3350104
21 J Howie, A proof of the Scott–Wiegold conjecture on free products of cyclic groups, J. Pure Appl. Algebra 173 (2002) 167 MR1915093
22 R Lipshitz, P S Ozsvath, D P Thurston, Bordered Heegaard Floer homology, 1216, Amer. Math. Soc. (2018) MR3827056
23 D Matignon, N Sayari, Longitudinal slope and Dehn fillings, Hiroshima Math. J. 33 (2003) 127 MR1966655
24 W W Menasco, M B Thistlethwaite, Surfaces with boundary in alternating knot exteriors, J. Reine Angew. Math. 426 (1992) 47 MR1155746
25 L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
26 Y Ni, Z Wu, Cosmetic surgeries on knots in S3, J. Reine Angew. Math. 706 (2015) 1 MR3393360
27 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
28 P Ozsváth, Z Szabó, Heegaard Floer homology and alternating knots, Geom. Topol. 7 (2003) 225 MR1988285
29 P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 MR2023281
30 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
31 P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 MR2113020
32 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
33 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
34 P Ozsváth, Z Szabó, On the Heegaard Floer homology of branched double-covers, Adv. Math. 194 (2005) 1 MR2141852
35 P S Ozsváth, Z Szabó, Knot Floer homology and integer surgeries, Algebr. Geom. Topol. 8 (2008) 101 MR2377279
36 I Petkova, Cables of thin knots and bordered Heegaard Floer homology, Quantum Topol. 4 (2013) 377 MR3134023
37 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) MR2704683
38 N Sayari, The reducibility of surgered 3-manifolds and homology 3-spheres, Topology Appl. 87 (1998) 73 MR1626088
39 M Scharlemann, Producing reducible 3-manifolds by surgery on a knot, Topology 29 (1990) 481 MR1071370
40 L G Valdez Sánchez, Dehn fillings of 3-manifolds and non-persistent tori, Topology Appl. 98 (1999) 355 MR1720012