Geometry & Topology Volume 27, issue 2 (2023)

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Convex cocompact actions of relatively hyperbolic groups

Mitul Islam and Andrew Zimmer

Geometry & Topology 27 (2023) 417–511

DOI: 10.2140/gt.2023.27.417

Bibliography

1	S A Ballas, J Danciger, G S Lee, Convex projective structures on nonhyperbolic three-manifolds, Geom. Topol. 22 (2018) 1593 MR3780442
2	Y Benoist, Convexes divisibles, II, Duke Math. J. 120 (2003) 97 MR2010735
3	Y Benoist, Convexes divisibles, I, from: "Algebraic groups and arithmetic" (editors S G Dani, G Prasad), Tata Inst. Fund. Res. (2004) 339 MR2094116
4	Y Benoist, Convexes divisibles, IV : Structure du bord en dimension 3, Invent. Math. 164 (2006) 249 MR2218481
5	Y Benoist, A survey on divisible convex sets, from: "Geometry, analysis and topology of discrete groups" (editors L Ji, K Liu, L Yang, S T Yau), Adv. Lect. Math. 6, International (2008) 1 MR2464391
6	J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR124005
7	M D Bobb, Codimension-1 simplices in divisible convex domains, Geom. Topol. 25 (2021) 3725 MR4372640
8	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9	H Busemann, P J Kelly, Projective geometry and projective metrics, Academic (1953) MR0054980
10	S Choi, G S Lee, L Marquis, Convex projective generalized Dehn filling, Ann. Sci. Éc. Norm. Supér. 53 (2020) 217 MR4093439
11	D Cooper, D D Long, S Tillmann, On convex projective manifolds and cusps, Adv. Math. 277 (2015) 181 MR3336086
12	J Danciger, F Guéritaud, F Kassel, Convex cocompact actions in real projective geometry, preprint (2017) arXiv:1704.08711
13	J Danciger, F Guéritaud, F Kassel, Convex cocompactness in pseudo-Riemannian hyperbolic spaces, Geom. Dedicata 192 (2018) 87 MR3749424
14	C Druţu, Quasi-isometry invariants and asymptotic cones, Internat. J. Algebra Comput. 12 (2002) 99 MR1902363
15	C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
16	S Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989) 109 MR1007621
17	D Gromoll, J A Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77 (1971) 545 MR281122
18	P de la Harpe, On Hilbert’s metric for simplices, from: "Geometric group theory, I" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 97 MR1238518
19	G C Hruska, Geometric invariants of spaces with isolated flats, Topology 44 (2005) 441 MR2114956
20	G C Hruska, B Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005) 1501 MR2175151
21	M Islam, A Zimmer, A flat torus theorem for convex co-compact actions of projective linear groups, J. Lond. Math. Soc. 103 (2021) 470 MR4230908
22	M Kapovich, Convex projective structures on Gromov–Thurston manifolds, Geom. Topol. 11 (2007) 1777 MR2350468
23	M Kapovich, B Leeb, Relativizing characterizations of Anosov subgroups, I, preprint (2018) arXiv:1807.00160
24	P Kelly, E Straus, Curvature in Hilbert geometries, Pacific J. Math. 8 (1958) 119 MR96261
25	B Kleiner, B Leeb, Rigidity of invariant convex sets in symmetric spaces, Invent. Math. 163 (2006) 657 MR2207236
26	H B Lawson Jr., S T Yau, Compact manifolds of nonpositive curvature, J. Differential Geometry 7 (1972) 211 MR334083
27	L Marquis, Around groups in Hilbert geometry, from: "Handbook of Hilbert geometry" (editors A Papadopoulos, M Troyanov), IRMA Lect. Math. Theor. Phys. 22, Eur. Math. Soc. (2014) 207 MR3329882
28	R D Nussbaum, Hilbert’s projective metric and iterated nonlinear maps, 391, Amer. Math. Soc. (1988) MR961211
29	J F Quint, Groupes convexes cocompacts en rang supérieur, Geom. Dedicata 113 (2005) 1 MR2171296
30	J F Quint, Convexes divisibles (d’après Yves Benoist), from: "Séminaire Bourbaki 2008/2009", Astérisque 332, Soc. Math. France (2010) 45 MR2648674
31	A Sisto, Projections and relative hyperbolicity, Enseign. Math. 59 (2013) 165 MR3113603
32	C Vernicos, On the Hilbert geometry of convex polytopes, from: "Handbook of Hilbert geometry" (editors A Papadopoulos, M Troyanov), IRMA Lect. Math. Theor. Phys. 22, Eur. Math. Soc. (2014) 111 MR3329878
33	D T Wise, Non-positively curved squared complexes : Aperiodic tilings and non-residually finite groups, PhD thesis, Princeton University (1996) MR2694733
34	F Zhu, Relatively dominated representations, preprint (2019) arXiv:1912.13152
35	A Zimmer, Projective Anosov representations, convex cocompact actions, and rigidity, J. Differential Geom. 119 (2021) 513 MR4333029