English

$\ell^2$-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 2\ell^2-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