ℓ² Betti numbers and coherence of random groups

2020/03/13 by Dawid Kielak, Kielak, Dawid, Robert Kropholler +3 · 1 citation
Mathematics · #16S35 #20E25 (Secondary) #20J05 (Primary) #20P05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:16S35 #msc:20E25 #msc:20J05 #msc:20P05

paper · pdf · doi:10.48550/arxiv.2003.06354

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

arxiv created 2022/06/14 · arxiv updated 2022/06/15

Abstract

We study ℓ² 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 ℓ² 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.

Cited by

• The word problem for two-generator one-relator inverse monoids

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