The RO(G)-graded Serre Spectral Sequence

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Title: The RO(G)-graded Serre Spectral Sequence
Author: Kronholm, William C., 1980-
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.
URI: http://hdl.handle.net/1794/8284
Date: 2008-06


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