Algebraic & Geometric Topology Volume 14, issue 2 (2014)

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Geodesic systems of tunnels in hyperbolic $3$–manifolds

Stephan D Burton and Jessica S Purcell

Algebraic & Geometric Topology 14 (2014) 925–952

DOI: 10.2140/agt.2014.14.925

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