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

Volume 30
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Morse actions of discrete groups on symmetric spaces: local-to-global principle

Michael Kapovich, Bernhard Leeb and Joan Porti

Geometry & Topology 29 (2025) 2343–2390
Bibliography
1 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, 61, Birkhäuser (1985) MR823981
2 G Baumslag, J E Roseblade, Subgroups of direct products of free groups, J. London Math. Soc. 30 (1984) 44 MR760871
3 Y Benoist, Propriétés asymptotiques des groupes linéaires, Geom. Funct. Anal. 7 (1997) 1 MR1437472
4 B H Bowditch, Spaces of geometrically finite representations, Ann. Acad. Sci. Fenn. Math. 23 (1998) 389 MR1642122
5 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
6 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 (1987) 3 MR903850
7 M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
8 K Corlette, Hausdorff dimensions of limit sets, I, Invent. Math. 102 (1990) 521 MR1074486
9 S Dey, M Kapovich, Klein–Maskit combination theorem for Anosov subgroups : free products, Math. Z. 305 (2023) 35 MR4647907
10 S Dey, M Kapovich, Klein–Maskit combination theorem for Anosov subgroups : amalgams, J. Reine Angew. Math. 819 (2025) 1 MR4856993
11 S Dey, M Kapovich, B Leeb, A combination theorem for Anosov subgroups, Math. Z. 293 (2019) 551 MR4002289
12 P B Eberlein, Geometry of nonpositively curved manifolds, Univ. Chicago Press (1996) MR1441541
13 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett (1992) MR1161694
14 J Gilman, Two-generator discrete subgroups of PSL(2, ), 561, Amer. Math. Soc. (1995) MR1290281
15 J Gilman, Algorithms, complexity and discreteness criteria in PSL(2, ), J. Anal. Math. 73 (1997) 91 MR1616469
16 J Gilman, L Keen, Canonical hexagons and the PSL(2, ) discreteness problem, preprint (2016) arXiv:1508.00257v3
17 J Gilman, B Maskit, An algorithm for 2-generator Fuchsian groups, Michigan Math. J. 38 (1991) 13 MR1091506
18 W M Goldman, Geometric structures on manifolds and varieties of representations, from: "Geometry of group representations" (editors W M Goldman, A R Magid), Contemp. Math. 74, Amer. Math. Soc. (1988) 169 MR957518
19 O Guichard, A Wienhard, Anosov representations: domains of discontinuity and applications, Invent. Math. 190 (2012) 357 MR2981818
20 H Izeki, Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures, Conform. Geom. Dyn. 4 (2000) 108 MR1799652
21 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
22 M Kapovich, Kleinian groups in higher dimensions, from: "Geometry and dynamics of groups and spaces" (editors M Kapranov, S Kolyada, Y I Manin, P Moree, L Potyagailo), Progr. Math. 265, Birkhäuser (2008) 487 MR2402415
23 M Kapovich, Discreteness is undecidable, Internat. J. Algebra Comput. 26 (2016) 467 MR3506344
24 M Kapovich, B Leeb, Discrete isometry groups of symmetric spaces, from: "Handbook of group actions, IV" (editors L Ji, A Papadopoulos, S T Yau), Adv. Lect. Math. 41, International (2018) 191 MR3888689
25 M Kapovich, B Leeb, Finsler bordifications of symmetric and certain locally symmetric spaces, Geom. Topol. 22 (2018) 2533 MR3811766
26 M Kapovich, B Leeb, Relativizing characterizations of Anosov subgroups, I, Groups Geom. Dyn. 17 (2023) 1005 MR4622401
27 M Kapovich, B Leeb, Relativizing characterizations of Anosov subgroups, II, in preparation
28 M Kapovich, B Liu, Geometric finiteness in negatively pinched Hadamard manifolds, Ann. Acad. Sci. Fenn. Math. 44 (2019) 841 MR3973544
29 M Kapovich, B Leeb, J Millson, Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weighted configurations at infinity, J. Differential Geom. 81 (2009) 297 MR2472176
30 M Kapovich, B Leeb, J Porti, Morse actions of discrete groups on symmetric space, preprint (2014) arXiv:1403.7671
31 M Kapovich, B Leeb, J Porti, Anosov subgroups: dynamical and geometric characterizations, Eur. J. Math. 3 (2017) 808 MR3736790
32 M Kapovich, B Leeb, J Porti, Dynamics on flag manifolds: domains of proper discontinuity and cocompactness, Geom. Topol. 22 (2018) 157 MR3720343
33 M Kapovich, B Leeb, J Porti, A Morse lemma for quasigeodesics in symmetric spaces and Euclidean buildings, Geom. Topol. 22 (2018) 3827 MR3890767
34 M Kapovich, S Kim, J Lee, Structural stability of meandering-hyperbolic group actions, J. Inst. Math. Jussieu 23 (2024) 753 MR4719151
35 F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 MR2221137
36 W L Lok, Deformations of locally homogeneous spaces and Kleinian groups, PhD thesis, Columbia Univ. (1984)
37 A Y Ol’shanskii, M V Sapir, Length and area functions on groups and quasi-isometric Higman embeddings, Internat. J. Algebra Comput. 11 (2001) 137 MR1829048
38 M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR507234
39 J M Riestenberg, A quantified local-to-global principle for Morse quasigeodesics, Groups Geom. Dyn. 19 (2025) 37
40 R Riley, Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra, Math. Comp. 40 (1983) 607 MR689477
41 D Sullivan, Quasiconformal homeomorphisms and dynamics, II : Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR806415
42 P Tukia, On isomorphisms of geometrically finite Möbius groups, Inst. Hautes Études Sci. Publ. Math. 61 (1985) 171 MR783351