L2-invisibility and a class of local similarity groups
Algebraic Topology
2019-02-20 v2 Group Theory
Abstract
In this note we show that the members of a certain class of local similarity groups are l2-invisible, i.e. the non-reduced group homology of the regular unitary representation vanishes in all degrees. This class contains for example Thompson's group V and Nekrashevych-R\"over groups. They yield counterexamples to a generalized zero-in-the-spectrum conjecture for groups that admit a classifying space with finitely many cells in each dimension.
Keywords
Cite
@article{arxiv.1304.6843,
title = {L2-invisibility and a class of local similarity groups},
author = {Roman Sauer and Werner Thumann},
journal= {arXiv preprint arXiv:1304.6843},
year = {2019}
}
Comments
only small changes and correction of typos; to appear in Compositio Math