Geodesic
On the product in negative Tate cohomology for finite groups
Tene, Haggai1
1Department of Mathematics and PMI, POSTECH, Pohang 790-784, South Korea
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 493-509
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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 BG:

for n,m > 0. 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 G is a compact Lie group (with an additional dimension shift).

DOI : 10.2140/agt.2012.12.493
Classification : 20J06, 55R40
Keywords: Tate cohomology, homology of classifying spaces, compact Lie group, product in homology, stratifold

Tene, Haggai  1

1 Department of Mathematics and PMI, POSTECH, Pohang 790-784, South Korea 
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Tene, Haggai. On the product in negative Tate cohomology for finite groups. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 493-509. doi: 10.2140/agt.2012.12.493

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[7] M Kreck, Differential algebraic topology : From stratifolds to exotic spheres, 110, Amer. Math. Soc. (2010)

[8] M Kreck, Pseudo homology, p–stratifold homology and ordinary homology, preprint (2011)

[9] H Tene, Stratifolds and equivariant cohomology theories, PhD thesis, University of Bonn (2010)

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