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

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.

33 pages. Version 2: this is the accepted version, minor typos and errors were corrected from Version 1. Comments are welcome!

References in corpus (1)

• Conformal dimension of hyperbolic groups that split over elementary subgroups