The RO(G)-graded Serre Spectral Sequence
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Date
2008-06
Authors
Kronholm, William C., 1980-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
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.
Description
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.
Keywords
Algebraic topology, Equivariant topology, Spectral sequence, Serre spectral sequence, Mathematics