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

Satoshi Tomoda and Peter Zvengrowski

Geometry & Topology Monographs 14 (2008) 519–556

DOI: 10.2140/gtm.2008.14.519

arXiv: 0904.1876

Abstract

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

Mathematical Subject Classification

Primary: 57M05, 57M60

Secondary: 20J06

References
Publication

Received: 6 August 2006
Accepted: 14 February 2007
Published: 29 April 2008

Authors
Satoshi Tomoda
Department of Mathematics and Statistics
Okanagan College
1000 KLO Road
Kelowna, B.C. V1Y 4X8
Canada
Peter Zvengrowski
Department of Mathematics and Statistics
University of Calgary
Calgary T2N 1N4
Canada