Amenable groups, topological entropy and Betti numbers

被引:6
作者
Elek, G [1 ]
机构
[1] Hungarian Acad Sci, Alfred Renyi Math Inst, H-1364 Budapest, Hungary
关键词
D O I
10.1007/BF02784519
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate an analogue of the L-2-Betti numbers for amenable linear subshifts. The role of the von Neumann dimension shall be played by the topological entropy.
引用
收藏
页码:315 / 335
页数:21
相关论文
共 21 条
[1]  
Atiyah M.F., 1976, ASTERISQUE, V32-33, P43
[2]   L2-COHOMOLOGY AND GROUP COHOMOLOGY [J].
CHEEGER, J ;
GROMOV, M .
TOPOLOGY, 1986, 25 (02) :189-215
[3]   VONNEUMANN DIMENSION AND THE HOMOLOGY OF COVERING SPACES [J].
COHEN, JM .
QUARTERLY JOURNAL OF MATHEMATICS, 1979, 30 (118) :133-142
[4]   Approximating L2 invariants of amenable covering spaces:: A combinatorial approach [J].
Dodziuk, J ;
Mathai, V .
JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 154 (02) :359-378
[5]   DE RHAM-HODGE THEORY FOR L2-COHOMOLOGY OF INFINITE COVERINGS [J].
DODZIUK, J .
TOPOLOGY, 1977, 16 (02) :157-165
[6]   The Euler characteristic of discrete groups and Yuzvinskii's entropy addition formula [J].
Elek, G .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1999, 31 :661-664
[7]  
Farber M, 1998, MATH ANN, V311, P335, DOI 10.1007/s002080050190
[8]  
HEWITT E, 1970, ABSTR HARMONIC ANAL, V2
[9]   AUTOMORPHISMS OF COMPACT-GROUPS [J].
KITCHENS, B ;
SCHMIDT, K .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1989, 9 :691-735
[10]   MAHLER MEASURE AND ENTROPY FOR COMMUTING AUTOMORPHISMS OF COMPACT-GROUPS [J].
LIND, D ;
SCHMIDT, K ;
WARD, T .
INVENTIONES MATHEMATICAE, 1990, 101 (03) :593-629