Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

The $RO(G)$-graded Serre spectral sequence

Pages: 75 – 92

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n1.a7

Author

William C. Kronholm (Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania, U.S.A.)

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 $G=\mathbb{Z}/2$ where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.

Keywords

spectral sequence; algebraic topology; local coefficient; equivariant homology and cohomology

2010 Mathematics Subject Classification

55N25, 55N91, 55T10

Full Text (PDF format)