Vanishing of l2-Betti numbers of locally compact groups as an invariant of coarse equivalence

被引：4

作者：

Sauer, Roman ^{[1
]}

Schroedl, Michael ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Inst Algebra & Geometry, Englerstr 2, D-76128 Karlsruhe, Germany

来源：

FUNDAMENTA MATHEMATICAE | 2018年 / 243卷 / 03期

关键词：

coarse geometry; locally compact groups; l(2)-Betti numbers; L-2-BETTI NUMBERS; APPROXIMATION; COHOMOLOGY;

D O I：

10.4064/fm512-1-2018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a proof that the vanishing of l(2)-Betti numbers of unimodular locally compact second countable groups is an invariant of coarse equivalence. To this end, we define coarse l(2)-cohomology for locally compact groups and show that it is isomorphic to continuous cohomology for unimodular groups and invariant under coarse equivalence.

引用

页码：301 / 311

页数：11

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