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

Dawid Kielak; Robert Kropholler; Gareth Wilkes

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

Group Theory 2022-06-15 v2

Authors: Dawid Kielak , Robert Kropholler , Gareth Wilkes

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.

Keywords

euler characteristic abelian groups random matrix ensembles

Cite

@article{arxiv.2003.06354,
  title  = {$\ell^2$ Betti numbers and coherence of random groups},
  author = {Dawid Kielak and Robert Kropholler and Gareth Wilkes},
  journal= {arXiv preprint arXiv:2003.06354},
  year   = {2022}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

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