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Abstract
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Our aim in this paper is to give a geometric description of the cup product
in negative degrees of Tate cohomology of a finite group with integral
coefficients. By duality it corresponds to a product in the integral homology of
:
for
.
We describe this product as join of cycles, which explains the shift in dimensions.
Our motivation came from the product defined by Kreck using stratifold homology.
We then prove that for finite groups the cup product in negative Tate cohomology
and the Kreck product coincide. The Kreck product also applies to the case where
is a
compact Lie group (with an additional dimension shift).
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Keywords
Tate cohomology, homology of classifying spaces, compact
Lie group, product in homology, stratifold
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Mathematical Subject Classification 2010
Primary: 20J06, 55R40
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Publication
Received: 3 April 2011
Revised: 24 November 2011
Accepted: 30 November 2011
Published: 21 March 2012
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