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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 groupH  1    (  G  ,  π  )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.

Group 1‐cohomology is complemented