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EQUIVARIANT ANDERSON DUALITY AND MACKEY FUNCTOR DUALITY

Part of: Topological $K$-theory Homology and cohomology theories

Published online by Cambridge University Press:  21 July 2015

NICOLAS RICKA
NICOLAS RICKA*
Affiliation:
Laboratoire Analyse, Géométrie et Applications, UMR 7539, 99, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France e-mail: [email protected]
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Abstract

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We show that the $\mathbb{Z}$/2-equivariant nth integral Morava K-theory with reality is self-dual with respect to equivariant Anderson duality. In particular, there is a universal coefficients exact sequence in integral Morava K-theory with reality, and we recover the self-duality of the spectrum KO as a corollary. The study of $\mathbb{Z}$/2-equivariant Anderson duality made in this paper gives a nice interpretation of some symmetries of RO($\mathbb{Z}$/2)-graded (i.e. bigraded) equivariant cohomology groups in terms of Mackey functor duality.

MSC classification

Primary: 55N91: Equivariant homology and cohomology
Secondary: 19L47: Equivariant $K$-theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 649 - 676
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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