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.
A refinement of Betti numbers in the presence of a continuous function, ( I )
Betti numbers of configuration spaces of surfaces
On the minimal sum of Betti numbers of an almost complex manifold
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