The RO(G)-Graded Serre Spectral Sequence

TL;DR

This paper extends the Serre spectral sequence to RO(G)-graded cohomology for finite groups, enabling new computations in equivariant topology, especially for G=Z/2, including projective bundles and loop spaces.

Contribution

It introduces an extension of the Serre spectral sequence to RO(G)-graded cohomology, broadening computational tools in equivariant topology.

Findings

Extended spectral sequence for RO(G)-graded cohomology.

Computed cohomology of specific projective bundles.

Analyzed loop spaces for G=Z/2.

Abstract

In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)-graded cohomology for finite groups G. Special attention is paid to the case G=Z/2 where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.