Computations based on explicit 4–periodic resolutions are given for
the cohomology of the finite groups G known to act freely on S3,
as well as the cohomology rings of the associated 3–manifolds
(spherical space forms) M = S3/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.
Keywords
cohomology ring, Seifert manifold,
spherical space form, fundamental group
