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_∞ .