Document Type

Article

Publication Date

1-1-2024

Abstract

Suppose a residually finite group G acts cocompactly on a contractible complex with strict fundamental domain Q, where the stabilizers are either trivial or have normal \BbbZ-subgroups. Let @Q be the subcomplex of Q with nontrivial stabilizers. Our main result is a computation of the homology torsion growth of a chain of finite index normal subgroups of G. We show that independent of the chain, the normalized torsion limits to the torsion of @Q shifted a degree. Under milder assumptions of acyclicity of nontrivial stabilizers, we show similar formulas for the mod p-homology growth. We also obtain formulas for the universal and the usual L2-torsion of G in terms of the torsion of stabilizers and topology of @Q. In particular, we get complete answers for right-angled Artin groups, which shows that they satisfy a torsion analogue of Lück’s approximation theorem.

Publication Source (Journal or Book title)

Duke Mathematical Journal

First Page

391

Last Page

418

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