Curvature criterion for vanishing of group cohomology

TL;DR

This paper presents a new geometric criterion that determines when the cohomology of BN-pair groups vanishes, especially for groups acting on non-thin affine buildings, providing sharp results.

Contribution

The paper introduces a novel geometric criterion for cohomology vanishing in BN-pair groups, improving understanding of their cohomological properties.

Findings

Establishes a sharp vanishing criterion for cohomology.

Applies to all BN-pair groups acting on non-thin affine buildings.

Provides new insights into the geometric aspects of group cohomology.

Abstract

We introduce a new geometric criterion for vanishing of cohomology for BN-pair groups. In particular, this new criterion yields a sharp vanishing of cohomology result for all BN-pair groups acting on non-thin affine building.