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.
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Schrödl-Baumann, M. \(\ell ^2\)-Betti numbers of random rooted simplicial complexes. manuscripta math. 162, 283–304 (2020). https://doi.org/10.1007/s00229-019-01131-y
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DOI: https://doi.org/10.1007/s00229-019-01131-y