Torsion homology growth and cheap rebuilding of inner-amenable groups
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1089-1105
Voir la notice de l'article provenant de la source EMS Press
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 l2-Betti number with arbitrary field coefficients and log-torsion in degree 1 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 q-normal subgroups.
Classification :
57M07, 43A07, 20E26
Mots-clés : cheap rebuilding, inner amenability, torsion homology growth, l2-Betti numbers
Mots-clés : cheap rebuilding, inner amenability, torsion homology growth, l2-Betti numbers
Affiliations des auteurs :
Matthias Uschold 1
Matthias Uschold. Torsion homology growth and cheap rebuilding of inner-amenable groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 1089-1105. doi: 10.4171/ggd/803
@article{10_4171_ggd_803,
author = {Matthias Uschold},
title = {Torsion homology growth and cheap rebuilding of~inner-amenable groups},
journal = {Groups, geometry, and dynamics},
pages = {1089--1105},
year = {2025},
volume = {19},
number = {3},
doi = {10.4171/ggd/803},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/803/}
}
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