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arXiv · 1810.09716

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

Michael Schrödl
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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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Michael Schrödl. 2018-10-23. $\ell^2$-Betti numbers of random rooted simplicial complexes. https://doi.org/10.1007/s00229-019-01131-y

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