${\ell }^2$ Betti numbers and coherence of random groups

Abstract

We study ${\ell }^2$ Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coherent, have ${\ell }^2$ homology concentrated in dimension 1, and embed in a virtually free-by-cyclic group with high probability. Similar results are shown with positive probability in the zero Euler characteristic case.

Revised version, accepted for publication. Includes slight strengthenings of main theorems

References in corpus (2)

• Criteria for virtual fibering
• Virtually abelian quotients of random groups