Banach Zuk's criterion for partite complexes with application to random groups

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Abstract

We prove a Banach version of \.Zuk's criterion for groups acting on partite 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.
Original languageEnglish
StatePublished - 6 Dec 2021

Keywords

  • math.GR
  • math.CO
  • math.FA
  • math.PR

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