论文信息 - Variants of Kazhdan’s property for subgroups of semisimple groups

Variants of Kazhdan’s property for subgroups of semisimple groups

Some variants of Kazhdan’s property (T) for discrete groups are presented. It is shown that some groups (e.g. SLn (Q),n≧3) which do not have property (T) still have some of these weaker properties. Applications to cohomology and infinitesimal rigidity for certain actions on manifolds are derived.

Alexander Lubotzky | Robert J. Zimmer | A. Lubotzky | R. Zimmer

[1] Jean-Pierre Serre,et al. Le Probleme des Groupes de Congruence Pour SL 2 , 1970 .

[2] R. Zimmer. Infinitesimal rigidity for smooth actions of discrete subgroups of Lie groups , 1990 .

[3] E. Wang. ON A MAXIMALITY PROPERTY OF DISCRETE SUBGROUPS WITH FUNDAMENTAL DOMAIN OF FINITE MEASURE. , 1967 .

[4] Robert Brooks,et al. Combinatorial problems in spectral geometry , 1986 .

[5] Peter Sarnak,et al. The arithmetic and geometry of some hyperbolic three manifolds , 1983 .

[6] Noga Alon,et al. lambda1, Isoperimetric inequalities for graphs, and superconcentrators , 1985, J. Comb. Theory, Ser. B.

[7] R. Zimmer. Representations of fundamental groups of manifolds with a semisimple transformation group , 1989 .

[8] Robert J. Zimmer,et al. Ergodic actions with generalized discrete spectrum , 1976 .

[9] Robert Brooks,et al. The spectral geometry of a tower of coverings , 1986 .

[10] R. Zimmer. Extensions of ergodic group actions , 1976 .

[11] K. Schmidt,et al. Coboundaries and Homomorphisms for Non‐Singular Actions and a Problem of H. Helson , 1980 .

[12] Robert J. Zimmer,et al. Kazhdan groups acting on compact manifolds , 1984 .

[13] Robert J. Zimmer,et al. Ergodic Theory and Semisimple Groups , 1984 .

[14] R. Zimmer. On the Cohomology of Ergodic Actions of Semisimple Lie Groups and Discrete Subgroups , 1981 .