INVARIANT EXPECTATIONS AND VANISHING OF BOUNDED COHOMOLOGY FOR EXACT GROUPS

被引：4

作者：

Douglas, Ronald G. ^{[1
]}

Nowak, Piotr W. ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2011年 / 3卷 / 01期

基金：

美国国家科学基金会;

关键词：

Exact group; bounded cohomology; Hochschild cohomology; convolution algebra; invariant expectation; CONTINUOUS BUNDLES; SPACES;

D O I：

10.1142/S1793525311000489

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a group. We apply this operator to show that exactness of a finitely generated group G implies the vanishing of the bounded cohomology of G with coefficients in a new class of modules, which are defined using the Hopf algebra structure of l(1)(G).

引用

页码：89 / 107

页数：19

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