Garland's method with Banach coefficients

Research output: Working paper/PreprintPreprint


We prove a Banach version of Garland's method of proving vanishing of cohomology for groups acting on simplicial complexes. The novelty of this new version is that our new condition applies to every reflexive Banach space. Using this new criteria we improve recent results regarding Banach fixed point theorems for random groups in the triangular model, give a sharp lower bound for the conformal dimension of the boundary of such groups, and derive new criteria for group stability with respect to p-Schatten norms.
Original languageEnglish
PublisherarXiv:2009.01234 [math.GR]
StatePublished - 2021


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