The cheap embedding principle: Dynamical upper bounds for homology growth

TL;DR

This paper establishes upper bounds on the growth of homology groups in terms of torsion and Betti numbers, using measured group theory to understand the limits of homology growth in groups.

Contribution

It introduces a novel approach to bounding homology growth using dynamical methods within measured group theory, providing new theoretical limits.

Findings

Upper bounds for homology growth established

Logarithmic torsion homology growth constrained

Betti number growth limits derived

Abstract

We provide upper bounds for logarithmic torsion homology growth and Betti number growth of groups, phrased in the language of measured group theory.