Recently several conjectures about l2-invariants of

CW-complexes have been disproved. At the heart of the counterexamples

is a method of computing the spectral measure of an element of the

complex group ring. We show that the same method can be used to

compute the finite field analog of the l2-Betti numbers, the homology

gradient. As an application we point out that (i) the homology

gradient over any field of characteristic different than 2 can be an

irrational number, and (ii) there exists a CW-complex whose homology

gradients over different fields have infinitely many different values.

11 November 2014

17:00

Lukasz Grabowski

Abstract