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Book Review

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Book Information

Author(s): Hyman Bass and Alexander Lubotzky
Title: Tree lattices
Additional book information: with appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits, Prog. Math., vol.176, Birkhäuser Boston, Inc., Boston, MA, 2001, xiv + 233, $54.95, ISBN 0-8176-4120-3

References:

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

[BL]
H. Bass and A. Lubotzky, Tree lattices, with appendices by Bass, L. Carbone, Lubotzky, G. Rosenberg and J. Tits. Progress in Mathematics, 176, Birkhauser Boston Inc., Boston, 2001. MR 2001k:20056

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[Bo]
A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2(1963), 111-122. MR 26:3823

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A. Borel, Introduction aux groupes arithmetiques, Hermann, Paris, 1969. MR 39:5577

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A. Borel and G. Harder, Existence of discrete cocompact subgroups of reductive groups over local fields, J. Reine Angew. Math. 298(1978), 53-64. MR 80b:22022

[BM1]
M. Burger and S. Mozes, Lattices in product of trees, Inst. Hautes Etudes Sci. Publ. Math., no.92(2000), 151-194(2001). MR 2002i:20042

[BM2]
M. Burger and S. Mozes, Groups acting on trees: from local to global structure, Inst. Hautes Etudes Sci. Publ. Math. no.92(2000), 113-150(2001). MR 2002i:20041

[BMZ]
M. Burger, S. Mozes and R. Zimmer, Irreducible lattices in the automorphism group of a product of trees, superrigidity and arithmeticity, in preparation.

[Ca1]
L. Carbone, Non-uniform lattices on uniform trees, Mem. Amer. Math. Soc. 152(2001), no. 724. MR 2002k:20045

[Ca2]
L. Carbone, Non-minimal actions and the existence of non-uniform tree lattices, in preparation.

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D. A. Kazhdan, On connection between the dual space of a group and the structure of its closed subgroups, Funct. Anal. Appl. 1(1967), 63-65.

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

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A. Lubotzky, Lattices in rank one Lie groups over local fields, Geom. Funct. Anal. 1(1991), 405-431. MR 92k:22019

[Lu2]
A. Lubotzky, Tree-lattices and lattices in Lie groups, Combinatorial and Geometric Group Theory (Edinburgh, 1993) 217-232, London Math. Soc. Lecture Notes Ser., 204, Cambridge Univ. Press, Cambridge, 1995.

[Ma]
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, Berlin, 1991. MR 92h:22021

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M. S. Raghunathan, Discrete subgroups of algebraic groups over local fields of positive characteristics, Proc. Indian Acad. Sci. Math. Sci. 99(1989), 127-146. MR 91a:22010

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J. P. Serre, Trees, Springer-Verlag, New York, 1980. MR 82c:20083

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T. Tamagawa, On discrete subgroups of $p$-adic algebraic groups, in Arithmetical Algebraic Geometry, O.F.G. Schilling (ed.), Harper and Row, New York, 1965, 11-17. MR 33:4060

Additional Information:

Reviewer(s):
Lucy Lifschitz
Affiliation: University of Oklahoma
Email: llifschitz@math.ou.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 40 (2003), 247-252.

MSC (2000): Primary 20E08
PII: S 0273-0979(03)00978-9
Posted: February 12, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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