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

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

2009-04-12

arxiv.org/abs/0904.1876v1

Geom. Topol. Monogr. 14 (2008) 519-556

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 29 April 2008

Scientific paper

10.2140/gtm.2008.14.519

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.

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