Algebraic & Geometric Topology Volume 21, issue 5 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Two-bridge knots admit no purely cosmetic surgeries

Kazuhiro Ichihara, In Dae Jong, Thomas W Mattman and Toshio Saito

Algebraic & Geometric Topology 21 (2021) 2411–2424

DOI: 10.2140/agt.2021.21.2411

Bibliography

1	H U Boden, C L Curtis, The SL(2, ℂ) Casson invariant for Dehn surgeries on two-bridge knots, Algebr. Geom. Topol. 12 (2012) 2095 MR3020202
2	S Boyer, D Lines, Surgery formulae for Casson’s invariant and extensions to homology lens spaces, J. Reine Angew. Math. 405 (1990) 181 MR1041002
3	T D Cochran, R E Gompf, Applications of Donaldson’s theorems to classical knot concordance, homology 3–spheres and property P, Topology 27 (1988) 495 MR976591
4	R Crowell, Genus of alternating link types, Ann. of Math. 69 (1959) 258 MR99665
5	C L Curtis, An intersection theory count of the SL₂(ℂ)–representations of the fundamental group of a 3–manifold, Topology 40 (2001) 773 MR1851563
6	J Hanselman, Heegaard Floer homology and cosmetic surgeries in S³, preprint (2019) arXiv:1906.06773
7	A Hatcher, W Thurston, Incompressible surfaces in 2–bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
8	K Ichihara, T Saito, Cosmetic surgery and the SL(2, ℂ) Casson invariant for two-bridge knots, Hiroshima Math. J. 48 (2018) 21 MR3771998
9	K Ichihara, Z Wu, A note on Jones polynomial and cosmetic surgery, Comm. Anal. Geom. 27 (2019) 1087 MR4037376
10	T Ito, On LMO invariant constraints for cosmetic surgery and other surgery problems for knots in S³, Comm. Anal. Geom. 28 (2020) 321 MR4101341
11	I D Jong, Alexander polynomials of alternating knots of genus two, Osaka J. Math. 46 (2009) 353 MR2549591
12	R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology, II" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
13	K Kishimoto, T Shibuya, T Tsukamoto, Sliceness of alternating pretzel knots and links, Topology Appl. 282 (2020) MR4123275
14	E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554 MR2173845
15	T W Mattman, G Maybrun, K Robinson, 2–bridge knot boundary slopes : diameter and genus, Osaka J. Math. 45 (2008) 471 MR2441951
16	W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
17	K Murasugi, On the genus of the alternating knot, I, J. Math. Soc. Japan 10 (1958) 94 MR99664
18	K Murasugi, On the genus of the alternating knot, II, J. Math. Soc. Japan 10 (1958) 235 MR99664
19	K Murasugi, On a certain subgroup of the group of an alternating link, Amer. J. Math. 85 (1963) 544 MR157375
20	L Neuwirth, The algebraic determination of the genus of knots, Amer. J. Math. 82 (1960) 791 MR120648
21	J H Przytycki, Positive knots have negative signature, Bull. Polish Acad. Sci. Math. 37 (1989) 559 MR1101920
22	A Stoimenow, Knots of genus one or on the number of alternating knots of given genus, Proc. Amer. Math. Soc. 129 (2001) 2141 MR1825928
23	A Stoimenow, Knots of (canonical) genus two, Fund. Math. 200 (2008) 1 MR2443760
24	P Traczyk, Nontrivial negative links have positive signature, Manuscripta Math. 61 (1988) 279 MR949818
25	P Traczyk, A combinatorial formula for the signature of alternating diagrams, Fund. Math. 184 (2004) 311 MR2128055