On the RO(G)-graded Equivariant Ordinary Cohomology of Generalized G-cell Complexes for G
Author: Kevin K. Ferland
Publisher:
Published: 1999
Total Pages: 176
ISBN-13:
DOWNLOAD EBOOKIt 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 = Z/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 Z/p actions. Our new result applies more generally to equivariant complex Grassmannians with linear Z/p actions.