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 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
Review Information:
Reviewer:
Lucy Lifschitz
Affiliation:
University of Oklahoma
Email:
llifschitz@math.ou.edu
Journal:
Bull. Amer. Math. Soc.
40 (2003), 247-252
Published electronically:
February 12, 2003
Review copyright:
© Copyright 2003
American Mathematical Society