On homology torsion growth
Miklos Abert
Alfréd Rényi Institute of Mathematics, Budapest, HungaryNicolas Bergeron
ENS / PSL University, Paris, FranceMikołaj Frączyk
University of Chicago, USADamien Gaboriau
CNRS / ENS de Lyon, France
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Abstract
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Farber sequences, in particular, along residual chains. For principal congruence subgroups, we also obtain strong asymptotic bounds for the torsion growth. As a central tool, we introduce a quantitative homotopical method called effective rebuilding. This constructs small classifying spaces of finite index subgroups, at the same time controlling the complexity of the homotopy. The method easily applies to free abelian groups and then extends recursively to a wide class of residually finite groups.
Cite this article
Miklos Abert, Nicolas Bergeron, Mikołaj Frączyk, Damien Gaboriau, On homology torsion growth. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1411