Equivariant local coefficients and the RO(G)-graded cohomology of classifying spaces

Abstract

This thesis consists of two main parts. In the second part, we recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local coefficients. We then show how to construct new equivariant analogues of these spectral sequences for RO(G)-graded Bredon homology and cohomology. Finally, we use these spectral sequences to complete a sample calculation, in which we use the equivariant Serre spectral sequence and the equivariant cohomology of complex projective spaces to compute the cohomology of the equivariant classifying space B_Cp O(2). However, to complete this sample computation, we need to know the cohomology of complex projective space. This calculation was done in a 1988 paper by Gaunce Lewis, but relies on a theorem whose proof as given was incorrect. We spend the first part of this thesis providing a correct proof and summarizing the results of Lewis's paper.

96 pages, 10 figures. This is the full text of the author's 2010 thesis. It includes the content of arxiv:1005.0379

References in corpus (1)

• The RO(G)-Graded Serre Spectral Sequence

Cited by in corpus (5)

• The freeness theorem for equivariant cohomology of Rep($C_2$)-complexes
• Real topological Hochschild homology of schemes
• The $RO(C_4)$ cohomology of the infinite real projective space
• Naive-commutative structure on rational equivariant $K$-theory for abelian groups
• $C_2$ equivariant characteristic classes over the rational Burnside ring