Żuk’s criterion for Banach spaces and random groups
We prove a Banach version of Żuk’s criterion for groups acting on partite (i.e., colorable) simplicial complexes. Using this new criterion, we derive a new fixed point theorem for random groups in the Gromov density model with respect to several classes of Banach spaces ( $L^p$ spaces, Hilbert...
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000804/type/journal_article |
| Summary: | We prove a Banach version of Żuk’s criterion for groups acting on partite (i.e., colorable) simplicial complexes. Using this new criterion, we derive a new fixed point theorem for random groups in the Gromov density model with respect to several classes of Banach spaces (
$L^p$
spaces, Hilbertian spaces, uniformly curved spaces). In particular, we show that for every p, a group in the Gromov density model has asymptotically almost surely property
$(F L^p)$
and give a sharp lower bound for the growth of the conformal dimension of the boundary of such group as a function of the parameters of the density model. |
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| ISSN: | 2050-5094 |