Book Review

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Book Information:

Authors: 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 pp., ISBN 0-8176-4120-3, $54.95

**[Ba]**H. Bass,*Covering theory for graphs of groups*, J. Pure Appl. Algebra**89**(1993), 3-47. MR**94j:20028****[BK]**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****[Be]**H. Behr,*Finite presentability of arithmetic groups over global function fields*, Proc. Edinburgh Math. Soc.**30**(1987), 23-39. MR**88f:11032****[Bo]**A. Borel,*Compact Clifford-Klein forms of symmetric spaces*, Topology**2**(1963), 111-122. MR**26:3823****[Bo2]**A. Borel,*Introduction aux groupes arithmetiques*, Hermann, Paris, 1969. MR**39:5577****[BH]**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.**[Ka]**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.**[Li]**Y. S. Liu,*Density of the commensurability groups of uniform tree lattices*, J. Algebra**165**(1994), 346-359. MR**95c:20036****[Lu1]**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****[Ra]**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****[Se]**J. P. Serre,*Trees*, Springer-Verlag, New York, 1980. MR**82c:20083****[Ta]**T. Tamagawa,*On discrete subgroups of -adic algebraic groups*, in Arithmetical Algebraic Geometry, O.F.G. Schilling (ed.), Harper and Row, New York, 1965, 11-17. MR**33:4060**

Review Information:

Reviewer: Lucy Lifschitz

Affiliation: University of Oklahoma

Email: llifschitz@math.ou.edu

Journal: Bull. Amer. Math. Soc.

**40**(2003), 247-252

MSC (2000): Primary 20E08

Published electronically: February 12, 2003

Review copyright: © Copyright 2003 American Mathematical Society