The cheap embedding principle: Dynamical upper bounds for homology growth

Kevin Li; Clara Loeh; Marco Moraschini; Roman Sauer; Matthias Uschold

The cheap embedding principle: Dynamical upper bounds for homology growth

Algebraic Topology 2025-08-06 v2 Dynamical Systems Group Theory Operator Algebras

Authors: Kevin Li , Clara Loeh , Marco Moraschini , Roman Sauer , Matthias Uschold

Abstract

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

Keywords

homology growth torsion Betti numbers measured group theory

Cite

@article{arxiv.2508.01347,
  title  = {The cheap embedding principle: Dynamical upper bounds for homology growth},
  author = {Kevin Li and Clara Loeh and Marco Moraschini and Roman Sauer and Matthias Uschold},
  journal= {arXiv preprint arXiv:2508.01347},
  year   = {2025}
}