AMENABILITY, KAZHDAN PROPERTY AND PERCOLATION FOR TREES, GROUPS AND EQUIVALENCE-RELATIONS

被引:24
作者
ADAMS, S [1 ]
LYONS, R [1 ]
机构
[1] INDIANA UNIV,DEPT MATH,BLOOMINGTON,IN 47405
关键词
D O I
10.1007/BF02776032
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove amenability for a broad class of equivalence relations which have trees associated to the equivalence classes. The proof makes crucial use of percolation on trees. We also discuss related concepts and results, including amenability of automorphism groups. A second main result is that no discrete subgroup of the automorphism group of a tree is isomorphic to the fundamental group of any closed manifold M admitting a nontrivial connection-preserving, volume-preserving action of a noncompact, simply connected, almost simple Lie group having Kazhdan's property (T). The technique of proof also shows that M does not admit a hyperbolic structure.
引用
收藏
页码:341 / 370
页数:30
相关论文
共 27 条
[1]   TREES AND AMENABLE EQUIVALENCE-RELATIONS [J].
ADAMS, S .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 :1-14
[2]   KAZHDAN GROUPS, COCYCLES AND TREES [J].
ADAMS, SR ;
SPATZIER, RJ .
AMERICAN JOURNAL OF MATHEMATICS, 1990, 112 (02) :271-287
[3]  
[Anonymous], 2003, TREES-STRUCT FUNCT
[4]  
Connes A, 1982, ERGOD THEOR DYN SYST, V1, P431, DOI DOI 10.1017/S014338570000136X
[5]   INVARIANT HILBERT DISTANCES ON HOMOGENEOUS SPACE [J].
FARAUT, J ;
HARZALLAH, K .
ANNALES DE L INSTITUT FOURIER, 1974, 24 (03) :171-217
[6]   ERGODIC EQUIVALENCE RELATIONS, COHOMOLOGY, AND VONNEUMANN ALGEBRAS .1. [J].
FELDMAN, J ;
MOORE, CC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 234 (02) :289-324
[7]  
Greenleaf F. P, 1969, J FUNCT ANAL, V4, P295, DOI DOI 10.1016/0022-1236(69)90016-0
[8]  
Grimmett G., 1989, PERCOLATION
[9]  
GROMOV M, 1988, RIGID TRANSFORMATION
[10]   AMENABLE EQUIVALENCE-RELATIONS AND TURING DEGREES [J].
KECHRIS, AS .
JOURNAL OF SYMBOLIC LOGIC, 1991, 56 (01) :182-194