Volume 14, issue 2 (2014)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Geodesic systems of tunnels in hyperbolic $3$–manifolds

Stephan D Burton and Jessica S Purcell

Algebraic & Geometric Topology 14 (2014) 925–952
Bibliography
1 C C Adams, Unknotting tunnels in hyperbolic $3$–manifolds, Math. Ann. 302 (1995) 177 MR1329452
2 C C Adams, A W Reid, Unknotting tunnels in two-bridge knot and link complements, Comment. Math. Helv. 71 (1996) 617 MR1420513
3 H Akiyoshi, M Sakuma, M Wada, Y Yamashita, Jørgensen's picture of punctured torus groups and its refinement, from: "Kleinian groups and hyperbolic $3$–manifolds" (editors Y Komori, V Markovic, C Series), London Math. Soc. Lecture Note Ser. 299, Cambridge Univ. Press (2003) 247 MR2044553
4 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098
5 J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
6 S D Burton, Unknotting tunnels of hyperbolic tunnel number $n$ manifolds, master’s thesis, Brigham Young University (2012)
7 R D Canary, M Culler, S Hersonsky, P B Shalen, Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups, J. Differential Geom. 64 (2003) 57 MR2015044
8 D Cooper, D Futer, J S Purcell, Dehn filling and the geometry of unknotting tunnels, Geom. Topol. 17 (2013) 1815 MR3073937
9 D Cooper, M Lackenby, J S Purcell, The length of unknotting tunnels, Algebr. Geom. Topol. 10 (2010) 637 MR2606795
10 M Culler, P B Shalen, Varieties of group representations and splittings of $3$–manifolds, Ann. of Math. 117 (1983) 109 MR683804
11 D B A Epstein, C Petronio, An exposition of Poincaré's polyhedron theorem, Enseign. Math. 40 (1994) 113 MR1279064
12 J Hempel, $3$–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
13 T Jørgensen, On cyclic groups of Möbius transformations, Math. Scand. 33 (1973) 250 MR0348103
14 T Jørgensen, On pairs of once-punctured tori, from: "Kleinian groups and hyperbolic $3$–manifolds" (editors Y Komori, V Markovic, C Series), London Math. Soc. Lecture Note Ser. 299, Cambridge Univ. Press (2003) 183 MR2044551
15 M Lackenby, J S Purcell, Geodesics and compression bodies, to appear in Experimental Mathematics arXiv:1302.3652
16 W B R Lickorish, A representation of orientable combinatorial $3$–manifolds, Ann. of Math. 76 (1962) 531 MR0151948
17 J Maher, S Schleimer, The handlebody complex, in preparation
18 A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. 99 (1974) 383 MR0349992
19 A Marden, Outer circles: An introduction to hyperbolic $3$–manifolds, Cambridge Univ. Press (2007) MR2355387
20 B Maskit, Kleinian groups, Grundl. Math. Wissen. 287, Springer (1988) MR959135
21 C McMullen, Cusps are dense, Ann. of Math. 133 (1991) 217 MR1087348
22 J W Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, from: "The Smith conjecture" (editors J W Morgan, H Bass), Pure Appl. Math. 112, Academic Press (1984) 37 MR758464
23 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1990) MR1277811
24 M Scharlemann, Heegaard splittings of compact $3$–manifolds, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 921 MR1886684
25 M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
26 W P Thurston, The geometry and topology of $3$–manifolds, lecture notes, Princeton University (1978–1981)
27 M Wada, Opti, a program to visualize quasi-conformal deformations of once-punctured torus groups