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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