Weak notions of normality and vanishing up to rank in L2- cohomology

Uri Bader; Alex Furman; Roman Sauer

doi:10.1093/imrn/rnt029

Weak notions of normality and vanishing up to rank in L²- cohomology

Uri Bader
, Alex Furman
, Roman Sauer

Weizmann Institute of Science, Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We study vanishing results for L²-cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. As a consequence, we show that the L²-Betti numbers of SL_n(R) for any infinite integral domain R vanish below degree n-1. Another application is the vanishing of all L²-Betti numbers for Thompson's groups F and T.

Original language	English
Pages (from-to)	3177-3189
Number of pages	13
Journal	International Mathematics Research Notices
Volume	2014
Issue number	12
DOIs	https://doi.org/10.1093/imrn/rnt029
State	Published - 1 Mar 2014

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnt029

https://arxiv.org/abs/1206.4793License: Other

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abstract = "We study vanishing results for L2-cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. As a consequence, we show that the L2-Betti numbers of SLn(R) for any infinite integral domain R vanish below degree n-1. Another application is the vanishing of all L2-Betti numbers for Thompson's groups F and T.",

author = "Uri Bader and Alex Furman and Roman Sauer",

note = "Funding Information: This work was supported in part by the BSF grant 2008267 (to U.B. and A.F.), the ISF grant 704/08 Funding Information: (to U.B)., and the NSF grants DMS 0604611 and 0905977 (A.F.), and the DFG grant 1661/3-1 (R.S.).",

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N2 - We study vanishing results for L2-cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. As a consequence, we show that the L2-Betti numbers of SLn(R) for any infinite integral domain R vanish below degree n-1. Another application is the vanishing of all L2-Betti numbers for Thompson's groups F and T.

AB - We study vanishing results for L2-cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. As a consequence, we show that the L2-Betti numbers of SLn(R) for any infinite integral domain R vanish below degree n-1. Another application is the vanishing of all L2-Betti numbers for Thompson's groups F and T.

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DO - 10.1093/imrn/rnt029

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 12

ER -

Weak notions of normality and vanishing up to rank in L²- cohomology

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