A spectral sequence to compute L2-Betti numbers of groups and groupoids
Abstract
We construct a spectral sequence for L2-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More generally, we obtain a permanence result for the Hopf-Singer conjecture under taking fiber bundles whose base space is an aspherical manifold with poly-surface fundamental group. As further sample applications of the spectral sequence, we obtain new vanishing theorems and explicit computations of L2-Betti numbers of groups and manifolds and obstructions to the existence of normal subrelations in measured equivalence relations.
Cite
@article{arxiv.0707.0906,
title = {A spectral sequence to compute L2-Betti numbers of groups and groupoids},
author = {Roman Sauer and Andreas Thom},
journal= {arXiv preprint arXiv:0707.0906},
year = {2014}
}
Comments
added remark 4.9 about applying spectral sequence in a non-ergodic situation; minor corrections