Group 1-cohomology is complemented
classification
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cohomologycomplementedgroupspacesubspacebanachclosedcoboundaries
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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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