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Remarks on the cohomology of finite fundamental groups of
3–manifolds
Satoshi Tomoda and Peter Zvengrowski
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Geometry & Topology Monographs 14
(2008) 519–556
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Abstract
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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 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.
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Keywords
cohomology ring, Seifert manifold,
spherical space form, fundamental group
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Mathematical Subject Classification
Primary: 57M05, 57M60
Secondary: 20J06
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Publication
Received: 6 August 2006
Accepted: 14 February 2007
Published: 29 April 2008
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