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The RO(G)-graded Serre Spectral Sequence

x, 72 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / The theory of equivariant homology and cohomology was first created by Bredon in his 1967 paper and has since been developed and generalized by May, Lewis, Costenoble, and a host of others. However, there has been a notable lack of computations done. In this paper, a version of the Serre spectral sequence of a fibration is developed for RO ( G )-graded equivariant cohomology of G -spaces for finite groups G . This spectral sequence is then used to compute cohomology of projective bundles and certain loop spaces.

In addition, the cohomology of Rep( G )-complexes, with appropriate coefficients, is shown to always be free. As an application, the cohomology of real projective spaces and some Grassmann manifolds are computed, with an eye towards developing a theory of equivariant characteristic classes. / Adviser: Daniel Dugger

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/8284
Date06 1900
CreatorsKronholm, William C., 1980-
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeThesis
RelationUniversity of Oregon theses, Dept. of Mathematics, Ph. D., 2008;

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