Group 1-cohomology is complemented

Abstract

We show a structural property of cohomology with coefficients in an isometric representation on a uniformly convex Banach space: if the cohomology group $H^1(G,\pi )$ is reduced, then, up to an isomorphism, it is a closed complemented, subspace of the space of cocycles and its complement is the subspace of coboundaries.

To appear in the Bulletin of the LMS

References in corpus (1)

• Property (T) and rigidity for actions on Banach spaces