Measure equivalence rigidity of the handlebody groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915128280088576 |
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| author | Hensel, Sebastian Horbez, Camille |
| author_facet | Hensel, Sebastian Horbez, Camille |
| contents | Let $V$ be a connected $3$-dimensional handlebody of finite genus at least $3$. We prove that the handlebody group $\mathrm{Mod}(V)$ is superrigid for measure equivalence, i.e. every countable group which is measure equivalent to $\mathrm{Mod}(V)$ is in fact virtually isomorphic to $\mathrm{Mod}(V)$. Applications include a rigidity theorem for lattice embeddings of $\mathrm{Mod}(V)$, an orbit equivalence rigidity theorem for free ergodic measure-preserving actions of $\mathrm{Mod}(V)$ on standard probability spaces, and a $W^*$-rigidity theorem among weakly compact group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10064 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Measure equivalence rigidity of the handlebody groups Hensel, Sebastian Horbez, Camille Group Theory Geometric Topology Operator Algebras Let $V$ be a connected $3$-dimensional handlebody of finite genus at least $3$. We prove that the handlebody group $\mathrm{Mod}(V)$ is superrigid for measure equivalence, i.e. every countable group which is measure equivalent to $\mathrm{Mod}(V)$ is in fact virtually isomorphic to $\mathrm{Mod}(V)$. Applications include a rigidity theorem for lattice embeddings of $\mathrm{Mod}(V)$, an orbit equivalence rigidity theorem for free ergodic measure-preserving actions of $\mathrm{Mod}(V)$ on standard probability spaces, and a $W^*$-rigidity theorem among weakly compact group actions. |
| title | Measure equivalence rigidity of the handlebody groups |
| topic | Group Theory Geometric Topology Operator Algebras |
| url | https://arxiv.org/abs/2111.10064 |