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arXiv · 1610.09188

Group 1-cohomology is complemented

Piotr W. Nowak
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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.

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Piotr W. Nowak. 2016-10-28. Group 1-cohomology is complemented. https://doi.org/10.1112/blms.12018

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