${l}^{2}$-invisibility and a class of local similarity groups. (19th August 2014) - Sauer, Roman; Thumann, Werner
Abstract: In this note we show that the members of a certain class of local similarity groups are ${l}^{2}$ -invisible, i.e. the (non-reduced) group homology of the regular unitary representation vanishes in all degrees. This class contains groups of type ${F}_{∞ }$, e.g. Thompson's group $V$ and Nekrashevych–Röver groups. They yield counterexamples to a generalized zero-in-the-spectrum conjecture for groups of type ${F}_{∞ }$ .