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Commutator-stable representations of hyperbolic groups

Ulysse Remfort-Aurat

Algebraic & Geometric Topology 26 (2026) 2559–2588
Bibliography
1 M Bestvina, -trees in topology, geometry, and group theory, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland, Amsterdam (2002) 55 MR1886668
2 M Bourdon, Actions quasi-convexes d’un groupe hyperbolique : flot géodésique, PhD thesis, Université Paris-Sud (1993)
3 N Brady, Branched coverings of cubical complexes and subgroups of hyperbolic groups, J. London Math. Soc. (2) 60 (1999) 461 MR1724853
4 H Bray, G Tiozzo, A global shadow lemma and logarithm law for geometrically finite Hilbert geometries, J. Mod. Dyn. 21 (2025) 443 MR4953246
5 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
6 R D Canary, Dynamics on character varieties: a survey, from: "Handbook of group actions, II" (editors L Ji, A Papadopoulos, S T Yau), Adv. Lect. Math. (ALM) 32, International Press (2015) 175 MR3382028
7 M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
8 M Culler, J W Morgan, Group actions on -trees, Proc. London Math. Soc. (3) 55 (1987) 571 MR907233
9 T Delzant, Sous-groupes à deux générateurs des groupes hyperboliques, from: "Group theory from a geometrical viewpoint" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. (1991) 177 MR1170366
10 T Delzant, O Guichard, F Labourie, S Mozes, Well displacing representations and orbit maps, (2007) arXiv:0704.3499
11 F W Gehring, G J Martin, Discrete quasiconformal groups, I, Proc. London Math. Soc. (3) 55 (1987) 331 MR896224
12 É Ghys, Les groupes hyperboliques, from: "Séminaire Bourbaki, 1989/1990", Astérisque 189–190, Soc. Math. de France (1990) 203 MR1099877
13 W M Goldman, Mapping class group dynamics on surface group representations, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 189 MR2264541
14 G Italiano, B Martelli, M Migliorini, Hyperbolic 5-manifolds that fiber over S1, Invent. Math. 231 (2023) 1 MR4526820
15 I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
16 J Lee, B Xu, Bowditch’s Q-conditions and Minsky’s primitive stability, Trans. Amer. Math. Soc. 373 (2020) 1265 MR4068264
17 M D Lee, Dynamics on PSL(2, )-character varieties of certain hyperbolic 3-manifolds, PhD thesis, University of Michigan (2012) MR3094006
18 M Lee, Dynamics on the PSL(2, )-character variety of a twisted I-bundle, Groups Geom. Dyn. 9 (2015) 187 MR3343351
19 J Maher, Linear progress in the complex of curves, Trans. Amer. Math. Soc. 362 (2010) 2963 MR2592943
20 J Marché, M Wolff, The modular action on PSL2()-characters in genus 2, Duke Math. J. 165 (2016) 371 MR3457677
21 K Matsuzaki, Structural stability of Kleinian groups, Michigan Math. J. 44 (1997) 21 MR1439666
22 Y N Minsky, On dynamics of Out(Fn) on PSL2() characters, Israel J. Math. 193 (2013) 47 MR3038545
23 F Paulin, The Gromov topology on -trees, Topology Appl. 32 (1989) 197 MR1007101
24 F Paulin, Outer automorphisms of hyperbolic groups and small actions on -trees, from: "Arboreal group theory" (editor R C Alperin), Math. Sci. Res. Inst. Publ. 19, Springer (1991) 331 MR1105339
25 S Schlich, Equivalence of primitive-stable and Bowditch actions of the free group of rank two on Gromov-hyperbolic spaces, (2024) arXiv:2211.14546
26 C Series, Primitive stability and Bowditch’s BQ-condition are equivalent, (2019) arXiv:1901.01396
27 D Sullivan, Quasiconformal homeomorphisms and dynamics, II : Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR806415
28 N Tholozan, T Wang, Simple Anosov representations of closed surface groups, (2023) arXiv:2307.02934
29 P Tukia, Convergence groups and Gromov’s metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
30 J Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005) 187 MR2164775
31 T Wang, Anosov representations over closed subflows, Trans. Amer. Math. Soc. 376 (2023) 6177 MR4630773
32 D Xu, Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space, (2026) arXiv:2402.12294