Dynamical correspondences of $L^2$-Betti numbers

Abstract

We investigate dynamical analogues of the $L^2$-Betti numbers for modules over integral group ring of a discrete sofic group. In particular, we show that the $L^2$-Betti numbers exactly measure the failure of addition formula for dynamical invariants.

The main result is reformulated a little bit and the proof is more self-contained

References in corpus (1)

• Amenability of groups is characterized by Myhill's Theorem