Volume 26, issue 3 (2022)

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

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

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
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Effective bilipschitz bounds on drilling and filling

David Futer, Jessica S Purcell and Saul Schleimer

Geometry & Topology 26 (2022) 1077–1188
Bibliography
1 C C Adams, Waist size for cusps in hyperbolic 3–manifolds, Topology 41 (2002) 257 MR1876890
2 I Agol, Bounds on exceptional Dehn filling, Geom. Topol. 4 (2000) 431 MR1799796
3 I Agol, Volume change under drilling, Geom. Topol. 6 (2002) 905 MR1943385
4 I Agol, Tameness of hyperbolic 3–manifolds, preprint (2004) arXiv:math/0405568
5 M Baker, D Cooper, A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3–manifolds, J. Topol. 1 (2008) 603 MR2417445
6 S A Bleiler, C D Hodgson, J R Weeks, Cosmetic surgery on knots, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2, Geom. Topol. Publ. (1999) 23 MR1734400
7 J Boland, C Connell, J Souto, Volume rigidity for finite volume manifolds, Amer. J. Math. 127 (2005) 535 MR2141643
8 K Böröczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978) 243 MR512399
9 S Boyer, D Lines, Surgery formulae for Casson’s invariant and extensions to homology lens spaces, J. Reine Angew. Math. 405 (1990) 181 MR1041002
10 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
11 J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
12 J F Brock, K W Bromberg, Inflexibility, Weil–Peterson distance, and volumes of fibered 3–manifolds, Math. Res. Lett. 23 (2016) 649 MR3533189
13 J F Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups, II : The ending lamination conjecture, Ann. of Math. 176 (2012) 1 MR2925381
14 K Bromberg, Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives, J. Amer. Math. Soc. 17 (2004) 783 MR2083468
15 K Bromberg, Projective structures with degenerate holonomy and the Bers density conjecture, Ann. of Math. 166 (2007) 77 MR2342691
16 K Bromberg, The space of Kleinian punctured torus groups is not locally connected, Duke Math. J. 156 (2011) 387 MR2772066
17 D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3–manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
18 D Cooper, D Futer, J S Purcell, Dehn filling and the geometry of unknotting tunnels, Geom. Topol. 17 (2013) 1815 MR3073937
19 M Culler, P B Shalen, Paradoxical decompositions, 2–generator Kleinian groups, and volumes of hyperbolic 3–manifolds, J. Amer. Math. Soc. 5 (1992) 231 MR1135928
20 M Culler, P B Shalen, Margulis numbers for Haken manifolds, Israel J. Math. 190 (2012) 445 MR2956250
21 R Detcherry, A quantum obstruction to purely cosmetic surgeries, preprint (2021) arXiv:2102.11323
22 D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
23 D Futer, J S Purcell, S Schleimer, Excluding cosmetic surgeries using hyperbolic geometry, in preparation
24 D Futer, J S Purcell, S Schleimer, Effective distance between nested Margulis tubes, Trans. Amer. Math. Soc. 372 (2019) 4211 MR4009389
25 D Futer, J S Purcell, S Schleimer, Effective drilling and filling of tame hyperbolic 3–manifolds, preprint (2021) arXiv:2104.09983
26 D Gabai, On the geometric and topological rigidity of hyperbolic 3–manifolds, J. Amer. Math. Soc. 10 (1997) 37 MR1354958
27 D Gabai, G R Meyerhoff, N Thurston, Homotopy hyperbolic 3–manifolds are hyperbolic, Ann. of Math. 157 (2003) 335 MR1973051
28 C M Gordon, Dehn surgery on knots, from: "Proceedings of the International Congress of Mathematicians, I" (editor I Satake), Math. Soc. Japan (1991) 631 MR1159250
29 J Hanselman, Heegaard Floer homology and cosmetic surgeries in S3, J. Eur. Math. Soc. (2022)
30 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
31 C D Hodgson, S P Kerckhoff, Harmonic deformations of hyperbolic 3–manifolds, from: "Kleinian groups and hyperbolic 3–manifolds" (editors Y Komori, V Markovic, C Series), Lond. Math. Soc. Lect. Note Ser. 299, Cambridge Univ. Press (2003) 41 MR2044544
32 C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. 162 (2005) 367 MR2178964
33 C D Hodgson, S P Kerckhoff, The shape of hyperbolic Dehn surgery space, Geom. Topol. 12 (2008) 1033 MR2403805
34 J Hoste, M Thistlethwaite, J Weeks, The first 1701936 knots, Math. Intelligencer 20 (1998) 33 MR1646740
35 K Ichihara, I D Jong, Cosmetic banding on knots and links, Osaka J. Math. 55 (2018) 731 MR3862782
36 K Ichihara, Z Wu, A note on Jones polynomial and cosmetic surgery, Comm. Anal. Geom. 27 (2019) 1087 MR4037376
37 B Jeon, The Zilber–Pink conjecture and the generalized cosmetic surgery conjecture, preprint (2018) arXiv:1801.07819
38 R Kirby, Problems in low-dimensional topology, from: "Geometric topology", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
39 T Kobayashi, Y Rieck, A linear bound on the tetrahedral number of manifolds of bounded volume (after Jørgensen and Thurston), from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 27 MR2866921
40 M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
41 W B R Lickorish, A representation of orientable combinatorial 3–manifolds, Ann. of Math. 76 (1962) 531 MR151948
42 A D Magid, Deformation spaces of Kleinian surface groups are not locally connected, Geom. Topol. 16 (2012) 1247 MR2967052
43 R Meyerhoff, A lower bound for the volume of hyperbolic 3–manifolds, Canad. J. Math. 39 (1987) 1038 MR918586
44 Y N Minsky, The classification of punctured-torus groups, Ann. of Math. 149 (1999) 559 MR1689341
45 Y Minsky, The classification of Kleinian surface groups, I : Models and bounds, Ann. of Math. 171 (2010) 1 MR2630036
46 H Namazi, J Souto, Non-realizability and ending laminations: proof of the density conjecture, Acta Math. 209 (2012) 323 MR3001608
47 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
48 Y Ni, Z Wu, Cosmetic surgeries on knots in S3, J. Reine Angew. Math. 706 (2015) 1 MR3393360
49 K Ohshika, Kleinian groups which are limits of geometrically finite groups, 834, Amer. Math. Soc. (2005) MR2154090
50 K Ohshika, Realising end invariants by limits of minimally parabolic, geometrically finite groups, Geom. Topol. 15 (2011) 827 MR2821565
51 J S Purcell, Volumes of highly twisted knots and links, Algebr. Geom. Topol. 7 (2007) 93 MR2289805
52 J S Purcell, Cusp shapes under cone deformation, J. Differential Geom. 80 (2008) 453 MR2472480
53 J S Purcell, J Souto, Geometric limits of knot complements, J. Topol. 3 (2010) 759 MR2746337
54 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
55 P B Shalen, A generic Margulis number for hyperbolic 3–manifolds, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 103 MR2866926
56 P B Shalen, Small optimal Margulis numbers force upper volume bounds, Trans. Amer. Math. Soc. 365 (2013) 973 MR2995380
57 T Soma, Existence of ruled wrappings in hyperbolic 3–manifolds, Geom. Topol. 10 (2006) 1173 MR2255495
58 W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)
59 A H Wallace, Modifications and cobounding manifolds, Canad. J. Math. 12 (1960) 503 MR125588