Remarks on the cohomology of finite fundamental groups of 3-manifolds

Tomoda, Satoshi; Zvengrowski, Peter

Remarks on the cohomology of finite fundamental groups of 3-manifolds

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Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain approximations to the diagonal are constructed, and explicit contracting homotopies also constructed for the cases G is a generalized quaternion group, the binary tetrahedral group, or the binary octahedral group. Some applications are briefly discussed.
This is the version published by Geometry & Topology Monographs on 29 April 2008