A Freeness Theorem for RO(Z/2)-graded Cohomology

TL;DR

This paper proves that the RO(Z/2)-graded cohomology of specific Rep(Z/2)-complexes, including projective spaces and Grassmannians, is free over the cohomology of a point with  coefficients.

Contribution

It establishes a freeness theorem for RO(Z/2)-graded cohomology of certain complexes, expanding understanding of their algebraic structure.

Findings

Cohomology is always free over the point's cohomology for the studied complexes.

Includes classical spaces like projective spaces and Grassmann manifolds.

Results apply to the  coefficient Mackey functor.

Abstract

In this paper it is shown that the RO(Z/2)-graded cohomology of a certain class of Rep(Z/2)-complexes, which includes projective spaces and Grassmann manifolds, is always free as a module over the cohomology of a point when the coefficient Mackey functor is \underline{Z/2}.