Geometry & Topology Volume 29, issue 6 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Other MSP journals

Tunnel number one knots satisfy the Berge conjecture

Tao Li, Yoav Moriah and Tali Pinsky

Geometry & Topology 29 (2025) 3271–3343

DOI: 10.2140/gt.2025.29.3271

Bibliography

1	I Agol, Bounds on exceptional Dehn filling, Geom. Topol. 4 (2000) 431 MR1799796
2	K L Baker, The Poincaré homology sphere, lens space surgeries, and some knots with tunnel number two, Pacific J. Math. 305 (2020) 1 MR4077684
3	K L Baker, D Buck, A G Lecuona, Some knots in S¹ ×S² with lens space surgeries, Comm. Anal. Geom. 24 (2016) 431 MR3521314
4	K L Baker, B G Doleshal, N Hoffman, On manifolds with multiple lens space fillings, Bol. Soc. Mat. Mex. 20 (2014) 405 MR3264625
5	K L Baker, C Gordon, J Luecke, Bridge number, Heegaard genus and non-integral Dehn surgery, Trans. Amer. Math. Soc. 367 (2015) 5753 MR3347189
6	K L Baker, J E Grigsby, M Hedden, Grid diagrams for lens spaces and combinatorial knot Floer homology, Int. Math. Res. Not. 2008 (2008) MR2429242
7	J Berge, Some knots with surgeries yielding lens spaces, preprint (1990) arXiv:1802.09722
8	J Berge, The knots in D² × S¹ which have nontrivial Dehn surgeries that yield D² × S¹, Topology Appl. 38 (1991) 1 MR1093862
9	J Berge, The simple closed curves in genus two Heegaard surfaces of S³ which are double-primitives, unpublished manuscript (2010)
10	S A Bleiler, C D Hodgson, Spherical space forms and Dehn filling, Topology 35 (1996) 809 MR1396779
11	S A Bleiler, R A Litherland, Lens spaces and Dehn surgery, Proc. Amer. Math. Soc. 107 (1989) 1127 MR984783
12	F Bonahon, J P Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. École Norm. Sup. 16 (1983) 451 MR740078
13	S Boyer, X Zhang, On Culler–Shalen seminorms and Dehn filling, Ann. of Math. 148 (1998) 737 MR1670053
14	M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
15	D Gabai, Foliations and the topology of 3-manifolds, III, J. Differential Geom. 26 (1987) 479 MR910018
16	D Gabai, Surgery on knots in solid tori, Topology 28 (1989) 1 MR991095
17	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
18	C M Gordon, J Luecke, Reducible manifolds and Dehn surgery, Topology 35 (1996) 385 MR1380506
19	J E Greene, The lens space realization problem, Ann. of Math. 177 (2013) 449 MR3010805
20	D J Heath, H J Song, Unknotting tunnels for P(−2,3,7), J. Knot Theory Ramifications 14 (2005) 1077 MR2196648
21	T Homma, M Ochiai, M o Takahashi, An algorithm for recognizing S³ in 3-manifolds with Heegaard splittings of genus two, Osaka Math. J. 17 (1980) 625 MR591141
22	R Kirby, Problems in low-dimensional topology, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2.2, Amer. Math. Soc. (1997) 35 MR1470751
23	M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
24	M Lackenby, R Meyerhoff, The maximal number of exceptional Dehn surgeries, Invent. Math. 191 (2013) 341 MR3010379
25	L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
26	S Negami, K Okita, The splittability and triviality of 3-bridge links, Trans. Amer. Math. Soc. 289 (1985) 253 MR779063
27	Y Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007) 577 MR2357503
28	M Ochiai, Heegaard diagrams and Whitehead graphs, Math. Sem. Notes Kobe Univ. 7 (1979) 573 MR567245
29	P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
30	J Rasmussen, Lens space surgeries and L-space homology spheres, preprint (2007) arXiv:0710.2531
31	T Saito, A note on lens space surgeries : orders of fundamental groups versus Seifert genera, J. Knot Theory Ramifications 20 (2011) 617 MR2796231
32	M Tange, Lens spaces given from L-space homology 3-spheres, Exp. Math. 18 (2009) 285 MR2555699
33	M Tange, A complete list of lens spaces constructed by Dehn surgery, I, preprint (2010) arXiv:1005.3512
34	W T Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
35	S C Wang, Cyclic surgery on knots, Proc. Amer. Math. Soc. 107 (1989) 1091 MR984820
36	Y Q Wu, Cyclic surgery and satellite knots, Topology Appl. 36 (1990) 205 MR1070700