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


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


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.


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

2010 Mathematics Subject Classification

55N25, 55N91, 55T10

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Published 1 January 2010