Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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K. Li - C. Loeh - M. Moraschini - R. Sauer - M. Uschold

The algebraic cheap rebuilding property

created by moraschini on 30 Oct 2024

[BibTeX]

preprint

Inserted: 30 oct 2024
Last Updated: 30 oct 2024

Year: 2024

ArXiv: 2409.05774 PDF

Abstract:

We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include algebraic finiteness properties, $\ell^2$-invisibility, $\ell^2$-acyclicity, lower bounds for Novikov--Shubin invariants, and vanishing of homology growth. We introduce an algebraic version of Ab\'ert--Bergeron--Fr\k{a}czyk--Gaboriau's cheap rebuilding property that implies vanishing of torsion homology growth and admits a combination theorem. As an application, we show that certain graphs of groups with amenable vertex groups and elementary amenable edge groups have vanishing torsion homology growth.

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