L2-invisibility and a class of local similarity groups

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-Röver 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.

only small changes and correction of typos; to appear in Compositio Math

References in corpus (2)

• On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
• Local similarities and the Haagerup property

Cited by in corpus (2)

• Operad groups as a unified framework for Thompson-like groups
• L2-invisibility of symmetric operad groups