On connective K-theory of elementary abelian 2-groups and local duality

Details On connective K-theory of elementary abelian 2-groups and local duality On connective K-theory of elementary abelian 2-groups and local duality

2011-12-29

arxiv.org/abs/1112.6327v1

Mathematics

Algebraic Topology

Scientific paper

The connective ku-(co)homology of elementary abelian 2-groups is determined as a functor of the elementary abelian 2-group. The argument requires only the calculation of the rank one case and the Atiyah-Segal theorem for KU-cohomology together with an analysis of the functorial structure of the integral group ring. The methods can also be applied to the odd primary case. These results are used to analyse the local cohomology spectral sequence calculating ku-homology, via a functorial version of local duality for Koszul complexes. This gives a conceptual explanation of results of Bruner and Greenlees.

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