Torsion homology growth and cheap rebuilding of inner-amenable groups

  • Matthias Uschold

    Universität Regensburg, Germany
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Abstract

We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Abért, Bergeron, Frączyk and Gaboriau. As a consequence, the first -Betti number with arbitrary field coefficients and log-torsion in degree vanish for these groups. This extends results previously known for amenable groups to inner-amenable groups. We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of -normal subgroups.

Cite this article

Matthias Uschold, Torsion homology growth and cheap rebuilding of inner-amenable groups. Groups Geom. Dyn. 19 (2025), no. 3, pp. 1089–1105

DOI 10.4171/GGD/803