Title

On the RO(G)-graded equivariant ordinary cohomology of generalized G-cell complexes for G = Z/p

Date of Award

1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

L. Gaunce Lewis, Jr.

Keywords

G-cell complexes, Equivariant, Cohomology

Subject Categories

Mathematics | Physical Sciences and Mathematics

Abstract

It is well known that the cohomology of a finite CW-complex with cells only in even dimensions is free. The equivariant analog of this result for generalized G -cell complexes is, however, not obvious, since RO ( G )-graded cohomology cannot be computed using cellular chains. We consider G = [Special characters omitted.] / p and study G -spaces that can be built as cell complexes using the unit disks of finite dimensional G -representations as cells. Our main result is that, if X is a G -complex containing only even dimensional representation cells and satisfying certain finite type assumptions, then the RO ( G )-graded equivariant ordinary cohomology is free as a graded module over the cohomology of a point. This extends a result due to Gaunce Lewis about equivariant complex projective spaces with linear [Special characters omitted.] / p actions. Our new result applies more generally to equivariant complex Grassmannians with linear [Special characters omitted.] / p actions.

Access

Surface provides description only. Full text is available to ProQuest subscribers. Ask your Librarian for assistance.

http://libezproxy.syr.edu/login?url=http://proquest.umi.com/pqdweb?did=730281581&sid=1&Fmt=2&clientId=3739&RQT=309&VName=PQD