Volume 17, issue 3 (2013)

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

Volume 24
Issue 7, 3219–3748
Issue 6, 2675–3218
Issue 5, 2149–2674
Issue 4, 1615–2148
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532

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 Interests
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
Dehn filling and the geometry of unknotting tunnels

Daryl Cooper, David Futer and Jessica S Purcell

Geometry & Topology 17 (2013) 1815–1876
Bibliography
1 C Adams, Unknotting tunnels in hyperbolic 3–manifolds, Math. Ann. 302 (1995) 177 MR1329452
2 C C Adams, Waist size for cusps in hyperbolic 3–manifolds, Topology 41 (2002) 257 MR1876890
3 C C Adams, Waist size for cusps in hyperbolic 3–manifolds, II, preprint available from the author (2002)
4 C C Adams, A W Reid, Unknotting tunnels in two-bridge knot and link complements, Comment. Math. Helv. 71 (1996) 617 MR1420513
5 H Akiyoshi, Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein–Penner’s method, Proc. Amer. Math. Soc. 129 (2001) 2431 MR1823928
6 H Akiyoshi, M Sakuma, M Wada, Y Yamashita, Punctured torus groups and 2–bridge knot groups, I, 1909, Springer (2007) MR2330319
7 D Bachman, Normalizing Heegaard–Scharlemann–Thompson splittings arXiv:math/0309049
8 R Benedetti, C Petronio, Lectures on hyperbolic geometry, , Springer (1992) MR1219310
9 S A Bleiler, C D Hodgson, Spherical space forms and Dehn filling, Topology 35 (1996) 809 MR1396779
10 S A Bleiler, Y Moriah, Heegaard splittings and branched coverings of B3, Math. Ann. 281 (1988) 531 MR958258
11 J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
12 B A Burton, Regina : normal surface and 3–manifold topology software
13 D Cooper, M Lackenby, J S Purcell, The length of unknotting tunnels, Algebr. Geom. Topol. 10 (2010) 637 MR2606795
14 M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3–manifolds
15 M Culler, P B Shalen, Margulis numbers for Haken manifolds, Israel J. Math. 190 (2012) 445 MR2956250
16 N M Dunfield, D P Thurston, A random tunnel number one 3-manifold does not fiber over the circle, Geom. Topol. 10 (2006) 2431 MR2284062
17 W Fenchel, Elementary geometry in hyperbolic space, 11, Walter de Gruyter & Co. (1989) MR1004006
18 D Futer, Involutions of knots that fix unknotting tunnels, J. Knot Theory Ramifications 16 (2007) 741 MR2341313
19 D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
20 D Futer, J S Purcell, Explicit Dehn filling and Heegaard splittings, Comm. Anal. Geom. 21 (2013) 625
21 F Guéritaud, Géométrie hyperbolique effective et triangulations idéales canoniques en dimension trois, PhD thesis, Université de Paris–XI (Orsay) (2006)
22 F Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006) 1239 MR2255497
23 F Guéritaud, S Schleimer, Canonical triangulations of Dehn fillings, Geom. Topol. 14 (2010) 193 MR2578304
24 R Guo, F Luo, Rigidity of polyhedral surfaces, II, Geom. Topol. 13 (2009) 1265 MR2496046
25 J Hass, Genus two Heegaard splittings, Proc. Amer. Math. Soc. 114 (1992) 565 MR1070519
26 D J Heath, H J Song, Unknotting tunnels for P(2,3,7), J. Knot Theory Ramifications 14 (2005) 1077 MR2196648
27 C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. 162 (2005) 367 MR2178964
28 M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
29 T Li, Heegaard surfaces and measured laminations, I : The Waldhausen conjecture, Invent. Math. 167 (2007) 135 MR2264807
30 M Lustig, Y Moriah, Are large distance Heegaard splittings generic ? arXiv:1002.4292
31 A D Magid, Deformation spaces of Kleinian surface groups are not locally connected, Geom. Topol. 16 (2012) 1247 MR2967052
32 J Maher, Random Heegaard splittings, J. Topol. 3 (2010) 997 MR2746344
33 R Meyerhoff, A lower bound for the volume of hyperbolic 3–manifolds, Canad. J. Math. 39 (1987) 1038 MR918586
34 Y Moriah, H Rubinstein, Heegaard structures of negatively curved 3-manifolds, Comm. Anal. Geom. 5 (1997) 375 MR1487722
35 H Moser, Proving a manifold to be hyperbolic once it has been approximated to be so, Algebr. Geom. Topol. 9 (2009) 103 MR2471132
36 W D Neumann, A W Reid, Arithmetic of hyperbolic manifolds, from: "Topology ’90" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 273 MR1184416
37 Y Rieck, E Sedgwick, Persistence of Heegaard structures under Dehn filling, Topology Appl. 109 (2001) 41 MR1804562
38 J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
39 M Sakuma, J Weeks, Examples of canonical decompositions of hyperbolic link complements, Japan. J. Math. 21 (1995) 393 MR1364387
40 M Scharlemann, Tunnel number one knots satisfy the Poenaru conjecture, Topology Appl. 18 (1984) 235 MR769294
41 M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
42 S Schleimer, Sphere recognition lies in NP, from: "Low-dimensional and symplectic topology" (editor M Usher), Proc. Sympos. Pure Math. 82, Amer. Math. Soc. (2011) 183
43 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
44 M Stocking, Almost normal surfaces in 3–manifolds, Trans. Amer. Math. Soc. 352 (2000) 171 MR1491877
45 W P Thurston, Three-dimensional geometry and topology, Vol. 1, 35, Princeton Univ. Press (1997) MR1435975
46 J L Tollefson, Involutions of sufficiently large 3–manifolds, Topology 20 (1981) 323 MR617370
47 F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR0224099