$\ell^2$-Betti numbers of random rooted simplicial complexes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866909404314468352 |
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| author | Schrödl, Michael |
| author_facet | Schrödl, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_09716 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | $\ell^2$-Betti numbers of random rooted simplicial complexes Schrödl, Michael Algebraic Topology 55U10, 05A16 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. |
| title | $\ell^2$-Betti numbers of random rooted simplicial complexes |
| topic | Algebraic Topology 55U10, 05A16 |
| url | https://arxiv.org/abs/1810.09716 |