On L^p-cohomology of semisimple groups and buildings

  • Tagungsort:

    Geb. 20.30, SR 2.058

  • Datum:

    20.06.2024

  • Referent:

    Antonio López Neumann

  • Zeit:

    15:45 Uhr

  • Abstract: L^p-cohomology is a fine quasi-isometry 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 Cornulier-Tessera 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 non-vanishing of L^p-cohomology in degree equal to the rank for non-Archimedean semisimple groups. An application of the same techniques allows us to obtain estimates on conformal dimension of hyperbolic buildings.