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Characterising slopes for hyperbolic knots and Whitehead doubles

Laura Wakelin

Algebraic & Geometric Topology 26 (2026) 625–657
Bibliography
1 I Agol, Bounds on exceptional Dehn filling, Geom. Topol. 4 (2000) 431 MR1799796
2 I Agol, The minimal volume orientable hyperbolic 2-cusped 3-manifolds, Proc. Amer. Math. Soc. 138 (2010) 3723 MR2661571
3 K L Baker, K Motegi, Noncharacterizing slopes for hyperbolic knots, Algebr. Geom. Topol. 18 (2018) 1461 MR3784010
4 J A Baldwin, S Sivek, Characterizing slopes for 52, J. Lond. Math. Soc. (2) 109 (2024) MR4760447
5 W R Brakes, Manifolds with multiple knot-surgery descriptions, Math. Proc. Cambridge Philos. Soc. 87 (1980) 443 MR556924
6 R Budney, JSJ-decompositions of knot and link complements in S3, Enseign. Math. (2) 52 (2006) 319 MR2300613
7 M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds
8 D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
9 D Futer, J S Purcell, S Schleimer, Effective bilipschitz bounds on drilling and filling, Geom. Topol. 26 (2022) 1077 MR4466646
10 D Gabai, 1-bridge braids in solid tori, Topology Appl. 37 (1990) 221 MR1082933
11 D Gabai, R Haraway, R Meyerhoff, N Thurston, A Yarmola, Hyperbolic 3-manifolds of low cusp volume, (2021) arXiv:2109.14570
12 C M Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983) 687 MR682725
13 C M Gordon, J Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987) 97 MR886439
14 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
15 C M Gordon, J Luecke, Dehn surgeries on knots creating essential tori, I, Comm. Anal. Geom. 3 (1995) 597 MR1371211
16 W H Jaco, P B Shalen, Seifert fibered spaces in 3-manifolds, 220, Amer. Math. Soc. (1979) MR539411
17 K Johannson, Homotopy equivalences of 3-manifolds with boundaries, 761, Springer (1979) MR551744
18 R Kirby, A calculus for framed links in S3, Invent. Math. 45 (1978) 35 MR467753
19 H Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresber. Dtsch. Math.-Ver. 38 (1929) 248
20 P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. (2) 165 (2007) 457 MR2299739
21 M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
22 M Lackenby, Every knot has characterising slopes, Math. Ann. 374 (2019) 429 MR3961316
23 M Lackenby, Dehn surgery from a hyperbolic perspective, lecture notes (2020)
24 M Lackenby, R Meyerhoff, The maximal number of exceptional Dehn surgeries, Invent. Math. 191 (2013) 341 MR3010379
25 W B R Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. (2) 76 (1962) 531 MR151948
26 B Mangum, T Stanford, Brunnian links are determined by their complements, Algebr. Geom. Topol. 1 (2001) 143 MR1823496
27 D McCoy, Non-integer characterizing slopes for torus knots, Comm. Anal. Geom. 28 (2020) 1647 MR4184829
28 J Milnor, A unique decomposition theorem for 3-manifolds, Amer. J. Math. 84 (1962) 1 MR142125
29 L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
30 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR385004
31 Y Ni, Z Wu, Cosmetic surgeries on knots in S3, J. Reine Angew. Math. 706 (2015) 1 MR3393360
32 Y Ni, X Zhang, Characterizing slopes for torus knots, Algebr. Geom. Topol. 14 (2014) 1249 MR3190593
33 P Ozsváth, Z Szabó, The Dehn surgery characterization of the trefoil and the figure eight knot, J. Symplectic Geom. 17 (2019) 251 MR3956375
34 P Sorya, Characterizing slopes for satellite knots, Adv. Math. 450 (2024) 109746 MR4755445
35 W Thurston, The geometry and topology of 3-manifolds, lecture notes (1978)
36 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982) 357 MR648524
37 A H Wallace, Modifications and cobounding manifolds, Canadian J. Math. 12 (1960) 503 MRMR125588