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2012 On the product in negative Tate cohomology for finite groups
Haggai Tene
Algebr. Geom. Topol. 12(1): 493-509 (2012). DOI: 10.2140/agt.2012.12.493


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:

H n ( B G , ) H m ( B G , ) H n + m + 1 ( B G , )

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).


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Haggai Tene. "On the product in negative Tate cohomology for finite groups." Algebr. Geom. Topol. 12 (1) 493 - 509, 2012.


Received: 3 April 2011; Revised: 24 November 2011; Accepted: 30 November 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1276.20059
MathSciNet: MR2916285
Digital Object Identifier: 10.2140/agt.2012.12.493

Primary: 20J06, 55R40

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 1 • 2012
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