The equivariant Thom isomorphism theorem (Q1183104)

The purpose of this paper is to extend ordinary \(RO(G)\)-graded cohomology to a theory graded on virtual \(G\)-bundles over a \(G\)-space and show that we can then prove a Thom isomorphism theorem for general \(G\)-vector bundles. The main idea is to use \textit{A. D. Elmendorf's} topologized spectra [J. Pure Appl. Algebra 54, 37-94 (1988; Zbl 0681.55007)]. Using the Thom isomorphism theorem, the authors give a new calculation of the additive structure of the equivariant cohomology of complex projective space for \(G=\mathbb{Z}/p\). In general, we are concerned with the recent result of \textit{L. G. Lewis jun.} [Lect. Notes Math. 1361, 53-122 (1988; Zbl 0669.57024)]; in the present paper, the authors also extend the calculation to a larger grading.