Approximating L^2 invariants of amenable covering spaces: A combinatorial approach

Abstract

In this paper, we prove that the $L^2$ Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, proving a conjecture that we made in an earlier paper. We also prove that an arbitrary amenable covering space of a finite simplicial complex is of determinant class.

14 pages, AMS-LaTeX, a minor revision of an earlier version containing new references to earlier work in the field

References in corpus (1)

• Approximating L^2 invariants of amenable covering spaces: A heat kernel approach