학술논문
$\ell^2$-Betti numbers of random rooted simplicial complexes
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Working Paper
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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.
Comment: Added references and Example 19; small corrections in the proof of Lemma 4
Comment: Added references and Example 19; small corrections in the proof of Lemma 4