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arXiv · 2204.05808

Top degree $\ell^p$-homology and conformal dimension of buildings

Antonio López Neumann
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Abstract

For a non-compact finite thickness building whose Davis apartment is an orientable pseudomanifold, we compute the supremum of the set of $p>1$ such that its top dimensional reduced $\ell^p$-cohomology is nonzero. We adapt the non-vanishing assertion of this result to any finite thickness building using the Bestvina realization. Using similar techniques, we generalize bounds obtained by Clais on the conformal dimension of some Gromov-hyperbolic buildings to any such building.

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Antonio López Neumann. 2022-04-12. Top degree $\ell^p$-homology and conformal dimension of buildings. https://doi.org/10.1007/s10711-024-00930-2

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