$\ell^2$-Betti numbers of random rooted simplicial complexes
Algebraic Topology
2024-11-27 v2
Abstract
We define unimodular measures on the space of rooted simplicial complexes and associate to each measure a chain complex and a trace function. As a consequence, we can define -Betti numbers of unimodular random rooted simplicial complexes and show that they are continuous under Benjamini-Schramm convergence.
Keywords
Cite
@article{arxiv.1810.09716,
title = {$\ell^2$-Betti numbers of random rooted simplicial complexes},
author = {Michael Schrödl},
journal= {arXiv preprint arXiv:1810.09716},
year = {2024}
}
Comments
Added references and Example 19; small corrections in the proof of Lemma 4