Reduced 1-cohomology and relative property (T)
type: Item
instance of: scholarly article
title: Reduced 1-cohomology and relative property (T)
zbMATH Open document ID: 1247.22009
author: Talia Fernós
author: Alain Valette
author: Florian Martin
published in: Mathematische Zeitschrift
publication date: 2012-05-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.1093
full work available at URL: T Fernos Reduced 2012.pdf
review text: Let \(G\) be a locally compact group. It is known that the Kazhdan's property (T) for a \(\sigma\)-compact \(G\) is equivalent to the vanishing of the first cohomology group \(H^1(G, \pi) = Z^1(G, \pi)/B^1(G, \pi)\) for every unitary representation \(\pi\), and for a compactly generated group \(G\), this is also equivalent to the vanishing of the first reduced cohomology group \({\overline H}^1(G, \pi) = Z^1(G, \pi)/{\overline B}^1(G, \pi)\) for every unitary representation \(\pi\). In this paper, the authors characterize group pairs having the property that the restriction map on all first reduced cohomology vanishes. It is also shown that this is inequivalent to relative property (T) even for compactly generated group pairs.
reviewed by: Tianxuan Miao
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 6031814
zbMATH Keywords: Kazhdan's property (T)
zbMATH Keywords: relative property (T)
zbMATH Keywords: first reduced cohomology
zbMATH Keywords: locally compact group
MaRDI profile type: Publication
OpenAlex ID: W2112955048
arXiv ID: 0912.1093
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DOI: 10.1007/S00209-010-0815-1
description: scientific article; zbMATH DE number 6031814