On L^pcohomology of semisimple groups and buildings

Venue:
Geb. 20.30, SR 2.058

Date:
20.06.2024

Speaker:
Antonio López Neumann

Time:
15:45 Uhr

Abstract: L^pcohomology is a fine quasiisometry invariant popularized by Gromov. In the case of semisimple groups, he expected it to vanish for all p>1 in degrees below the rank and to be nonzero in degree equal to the rank at least for some p>1. Pansu and CornulierTessera showed vanishing for all p>1 in degree 1 for all higher rank semisimple groups. We show that it is also the case in degree 2 for most semisimple groups of rank at least 3. We also obtain nonvanishing of L^pcohomology in degree equal to the rank for nonArchimedean semisimple groups. An application of the same techniques allows us to obtain estimates on conformal dimension of hyperbolic buildings.