Bulletin of the American Mathematical Society

Full text of review: PDF   This review is available free of charge.
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 0146301

[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

[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 0146301

[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