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Group representations in the homology of 3-manifolds

Group representations in the homology of 3-manifolds

If M is a manifold with an action of a group G , then the homology group H_1(M,\mathbb Q) is naturally a \mathbb Q[G] -module, where \mathbb Q[G] denotes the rational group ring. We prove that for every finite group G , and for every \mathbb Q[G] -module W , …