${\ell }^2$-Betti numbers of random rooted simplicial complexes

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 ${\ell }^2$-Betti numbers of unimodular random rooted simplicial complexes and show that they are continuous under Benjamini-Schramm convergence.

Added references and Example 19; small corrections in the proof of Lemma 4

References in corpus (1)

• $L^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices

Cited by in corpus (1)

• Unimodular measures on the space of all Riemannian manifolds