Volume 14, issue 4 (2014)

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

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Dynamics on the $\mathrm{PSL}(2,\mathbb{C})$–character variety of a compression body

Michelle Lee

Algebraic & Geometric Topology 14 (2014) 2149–2179
Bibliography
1 I Agol, Tameness of hyperbolic $3$–manifolds, arXiv:math/0405568
2 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
3 F Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. 124 (1986) 71 MR847953
4 J F Brock, Continuity of Thurston's length function, Geom. Funct. Anal. 10 (2000) 741 MR1791139
5 J F Brock, K W Bromberg, R D Canary, Y N Minsky, Local topology in deformation spaces of hyperbolic $3$–manifolds, Geom. Topol. 15 (2011) 1169 MR2831259
6 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
7 D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
8 R D Canary, Dynamics on character varieties: A survey, arXiv:1306.5832
9 R D Canary, Ends of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 6 (1993) 1 MR1166330
10 R D Canary, A covering theorem for hyperbolic $3$–manifolds and its applications, Topology 35 (1996) 751 MR1396777
11 R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press, Cambridge (1987) 3 MR903850
12 R D Canary, S Hersonsky, Ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic $3$–manifolds, Amer. J. Math. 126 (2004) 1193 MR2102392
13 R D Canary, A Magid, Dynamics on $\mathrm{PSL}(2,\mathbb{C})$–character varieties: $3$–manifolds with toroidal boundary components, arXiv:1110.6567
14 R D Canary, D McCullough, Homotopy equivalences of $3$–manifolds and deformation theory of Kleinian groups, Mem. Amer. Math. Soc. 812, Amer. Math. Soc. (2004) MR2096234
15 R D Canary, Y N Minsky, On limits of tame hyperbolic $3$–manifolds, J. Differential Geom. 43 (1996) 1 MR1424418
16 R D Canary, P A Storm, Moduli spaces of hyperbolic $3$–manifolds and dynamics on character varieties, Comment. Math. Helv. 88 (2013) 221 MR3008919
17 J W Cannon, W P Thurston, Group invariant Peano curves, Geom. Topol. 11 (2007) 1315 MR2326947
18 W J Floyd, Group completions and limit sets of Kleinian groups, Invent. Math. 57 (1980) 205 MR568933
19 T Gelander, Y N Minsky, The dynamics of $\mathrm{Aut}(\mathbb{F}_n)$ on redundant representations, Groups Geom. Dyn. 7 (2013) 557 MR3095709
20 I A Grushko, On the bases of a free product of groups, Mat. Sbornik 8 (1940) 169
21 T Hartnick, T Strubel, Cross ratios, translation lengths and maximal representations, Geom. Dedicata 161 (2012) 285 MR2994044
22 W Jeon, I Kim, Primitive stable representations of geometrically infinite handlebody hyperbolic $3$–manifolds, C. R. Math. Acad. Sci. Paris 348 (2010) 907 MR2677989
23 W Jeon, I Kim, C Lecuire, K Ohshika, Primitive stable representations of free Kleinian groups, arXiv:1003.2055
24 M Kapovich, Hyperbolic manifolds and discrete groups, Progress in Mathematics 183, Birkhäuser (2001) MR1792613
25 G Kleineidam, J Souto, Algebraic convergence of function groups, Comment. Math. Helv. 77 (2002) 244 MR1915041
26 A Kurosch, Die Untergruppen der freien Produkte von beliebigen Gruppen, Math. Ann. 109 (1934) 647 MR1512914
27 F Labourie, Cross ratios, Anosov representations and the energy functional on Teichmüller space, Ann. Sci. Éc. Norm. Supér. 41 (2008) 437 MR2482204
28 C Lecuire, An extension of the Masur domain, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 49 MR2258744
29 M Lee, Dynamics on the $\mathrm{PSL}(2,\mathbb{C})$–character variety of a twisted $I$–bundle, to appear in Groups, Geom. Dyn.
30 M Lee, Dynamics on $\mathrm{PSL}(2,\mathbb{C})$–character varieties of certain hyperbolic $3$–manifolds, PhD thesis, University of Michigan (2012)
31 J Marché, M Wolff, The modular action on $\mathrm{PSL}(2,\mathbb{R})$–characters in genus $2$, arXiv:1309.3553
32 A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. 99 (1974) 383 MR0349992
33 H Masur, Measured foliations and handlebodies, Ergodic Theory Dynam. Systems 6 (1986) 99 MR837978
34 D McCullough, Compact submanifolds of $3$–manifolds with boundary, Quart. J. Math. Oxford Ser. 37 (1986) 299 MR854628
35 D McCullough, A Miller, Homeomorphisms of $3$–manifolds with compressible boundary, Mem. Amer. Math. Soc. 344, Amer. Math. Soc. (1986) MR840832
36 Y N Minsky, On dynamics of $\mathrm{Out}(\mathbb{F}_n)$ on $\mathrm{PSL}_2(\mathbb{C})$ characters, Israel J. Math. 193 (2013) 47 MR3038545
37 M Mj, Cannon–Thurston Maps for Kleinian Groups, arXiv:1002.0996
38 H Namazi, J Souto, Nonrealizability and ending laminations: proof of the density conjecture, Acta Math. 209 (2012) 323 MR3001608
39 K Ohshika, Realising end invariants by limits of minimally parabolic, geometrically finite groups, Geom. Topol. 15 (2011) 827 MR2821565
40 J P Otal, Courants géodésiques et produits libres, Thése d’Etat, Université de Paris-Sud, Orsay (1988)
41 G P Scott, Compact submanifolds of $3$–manifolds, J. London Math. Soc. 7 (1973) 246 MR0326737
42 J R Stallings, Whitehead graphs on handlebodies, from: "Geometric group theory down under" (editors J Cossey, W D Neumann, M Shapiro), de Gruyter (1999) 317 MR1714852
43 D Sullivan, Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR806415
44 W P Thurston, Three-dimensional geometry and topology, Vol. 1 (editor S Levy), Princeton Mathematical Series 35, Princeton Univ. Press (1997) MR1435975
45 J H C Whitehead, On certain sets of elements in a free group, Proc. London Math. Soc. S2-41 (1935) 48 MR1575455
46 A Wienhard, The action of the mapping class group on maximal representations, Geom. Dedicata 120 (2006) 179 MR2252900