Vanishing of cohomology with coefficients in representations on Banach spaces of groups acting on Buildings

Abstract

We prove vanishing of cohomology with coefficients in representations on a large class of Banach spaces for a group acting "nicely" on a simplicial complexes based on spectral properties of the 1-dimensional links of the simplicial complex.

arXiv comment36 pages, extended and improved expotision, several small mistakes were corrected