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

  • Michael Schrödl-BaumannEmail author
Article
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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.

Mathematics Subject Classification

Primary 55U10 Secondary 57M10 

Notes

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Algebra and GeometryKarlsruhe Institute of TechnologyKarlsruheGermany

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