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CAT$(-1)$-spaces, divergence groups and their commensurators

Author(s): M. Burger; S. Mozes
Journal: J. Amer. Math. Soc. 9 (1996), 57-93.
MSC (1991): Primary 22D40, 20E08, 22E40
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References:

[A'C-B]
N. A'Campo and M. Burger, Réseaux arithmétiques et commensurateurs d'après G.A. Margulis, Invent. Math. 116 (1994), 1--25, CMP 94:05.

[Ad1]
S. Adams, Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups, Topology 33 (1994), 765--783, CMP 94:17.

[Ad2]
------, Reduction of cocycles with hyperbolic targets.

[Az]
R. Azencott, Espaces de Poisson des groupes localement compacts, Lecture Notes in Math., vol. 148, Springer, Berlin and New York, 1970, MR 58:18748.

[B]
W. Ballmann, Lectures on spaces of nonpositive curvature.

[B-G-S]
W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Progr. in Math., vol. 61, Birkhäuser, Boston, 1985.

[B-Br]
W. Ballmann and M. Brin, Polygonal complexes and combinatorial group theory, Geom. Dedicata 50 (1994), 165--191, MR 95e:57004.

[Ba]
H. Bass, Covering theory for graphs of groups, J. Pure Appl. Alg. 89 (1993), 3--47, MR 94j:20028.

[Ba-Ku]
H. Bass and R. Kulkarni, Uniform tree lattices, J. Amer. Math. Soc. 3 (1990), 843--902, MR 91k:20034.

[Ba-Lu1]
H. Bass and A. Lubotzky, Rigidity of group actions on locally finite trees, Proc. London Math. Soc. 64 (1994), 541--575, CMP 94:16.

[Ba-Lu2]
------, Tree lattices (In preparation).

[Be1]
N. Benakli, Polyèdres à géométrie locale donnée, C.R. Acad. Sci. Paris Sér. I 313 (1991), 561--564, MR 92k:52018.

[Be2]
------, Polyèdres hyperboliques à groupe d'automorphisme non discret, C.R. Acad. Sci. Paris Sér. I 313 (1991), 667--669, MR 93b:57005.

[Ber-Ze]
I.N. Bernstein and A.V. Zelevinski, Representations of the group GL$(n,F)$ where $F$ is a non-archimedean local field, Russian Math. Surveys 31 (3) (1976), 1--68, MR 54:12988.

[Bo]
A. Borel, Linear algebraic groups, Springer, Berlin and New York, 1991, MR 92d:20001.

[Bo-Sp]
A. Borel and T.A. Springer, Rationality properties of linear algebraic groups II, Tôhoku Math. J. 20 (1968), 443--497, MR 39:5576.

[Bo-Ti]
A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55--150, MR 34:7527.

[Bou]
M. Bourdon, Actions quasi-convexes d'un groupe hyperbolique, flot géodésique.

[Bow]
B.H. Bowditch, Some results on the geometry of convex hulls in manifolds of pinched negative curvature, Comment. Math. Helv. 69 (1994), 49--81, MR 94m:53044.

[Bri-Ha]
M. Bridson and A. Haefliger, Metric spaces of nonpositive curvature (In preparation).

[Co]
M. Coornaert, Mesures de Patterson--Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993), 241--270, MR 94m:57075.

[Co-Pa1]
M. Coornaert and A. Papadopoulos, Une dichotomie de Hopf pour les flots géodésiques associés aux groupes discrets d'isométries des arbres, Trans. Amer. Math. Soc. 343 (1994), 883--898, MR 94h:58131.

[Co-Pa2]
------, Récurrence de marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers, Strasbourg, 1994.

[Da]
M.W. Davis, Nonpositive curvature and reflection groups.

[Fu]
H. Furstenberg, A Poisson formula for semisimple Lie groups, Ann. of Math. (2) 77 (1963), 335--383, MR 26:3820.

[Gh-H]
E. Ghys and P. de la Harpe (eds.), Sur les groupes hyperboliques d'après Gromov, Progr. Math., vol. 83, Birkhäuser, Boston, 1990.

[Gr]
M. Gromov, Hyperbolic groups, Essays in Group Theory (S.M. Gersten, ed.), MR 89e:20070.

[Hag]
F. Haglund, Les polyèdres de Gromov.

[Ho1]
E. Hopf, Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung, Ber. Verh. Sächs. Akad. Wiss. Leipzig 91 (1933), 261--304.

[Ho2]
E. Hopf, Ergodic theory and the geodesic flow on surfaces of constant negative curvature, Bull. Amer. Math. Soc. 77 (1971), 863--877, MR 44:1789.

[Ka]
V. A. Kaimanovich, Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces, J. Reine Angew. Math. 455 (1994), 57--103, CMP 95:01.

[Li]
Y. Liu, Density of the commensurability group of uniform tree lattices, J. Algebra 165 (1994), 346--359, MR 95c:20036.

[L-M-Z]
A. Lubotzky, S. Mozes, and R.J. Zimmer, Superrigidity of the commensurability group of tree lattices, Comment. Math. Helv. 69 (1994), 523--548, CMP 95:04.

[Ma]
G.A. Margulis, Discrete subgroups of semisimple groups, Ergeb. Math. Grenzgeb. (3)17, Springer, Berlin and New York, 1991, MR 92h:22021.

[Mou]
G. Moussong, Hyperbolic Coxeter groups.

[Ni]
P.J. Nicholls, The ergodic theory of discrete groups, London Math. Soc. Lecture Notes, vol. 143, Cambridge Univ. Press, Cambridge and New York, 1989, MR 91i:58104.

[Pa]
S.J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), 241--273, MR 56:8841.

[Re]
H. Reiter, Classical harmonic analysis and locally compact groups, Oxford Univ. Press, London and New York, 1968, MR 46:5933.

[Se]
J.-P. Serre, Trees, Springer, Berlin and New York, 1980, MR 82c:20083.

[Su]
D. Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), 259--277, MR 86c:58093.

[Ti1]
J. Tits, Algebraic and abstract simple groups, Ann. of Math. (2) 80 (1964), 313--329, MR 29:2259.

[Ti2]
------, Sur le groupe des automorphismes d'un arbre, Essays on Topology and Related Topics: Memoires dédiés à Georges de Rham, Springer-Verlag, Berlin and New York, 1970, MR 45:8582.

[Va]
N.Th. Varapoulos, Analysis and geometry on groups, Proc. Internat. Congr. Math. (Kyoto 1990), 951--957.

[Zi1]
R. Zimmer, Curvature of leaves in amenable foliations, Amer. J. Math. 105 (1983), 1011--1022, MR 84k:58178.

[Zi2]
------, Amenable ergodic group actions and applications to Poisson boundaries of random walks, J. Funct. Anal. 27 (1978), 350--372, MR 57:12775.

[Zi3]
------, Ergodic theory and semisimple groups, Monographs in Math., vol. 81, Birk-
häuser, Boston, 1984, MR 86j:22014.

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Additional Information:

M. Burger
Affiliation: IMA, Université de Lausanne, Lausanne--Dorigny, Switzerland

S. Mozes
Affiliation: Department of Mathematics, Hebrew University, Jerusalem, Israel

DOI: 10.1090/S0894-0347-96-00196-8
PII: S 0894-0347(96)00196-8
Received by editor(s): November 18, 1993
Copyright of article: Copyright 1996, American Mathematical Society

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