## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 12, Number 1 (2010), 75-92.

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

#### 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.

#### Article information

**Source**

Homology Homotopy Appl., Volume 12, Number 1 (2010), 75-92.

**Dates**

First available in Project Euclid: 28 January 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1296223823

**Mathematical Reviews number (MathSciNet)**

MR2607411

**Zentralblatt MATH identifier**

1195.55014

**Subjects**

Primary: 55T10: Serre spectral sequences 55N25: Homology with local coefficients, equivariant cohomology 55N91: Equivariant homology and cohomology [See also 19L47]

**Keywords**

Spectral sequence algebraic topology local coefficient equivariant homology and cohomology

#### Citation

Kronholm, William C. The $RO(G)$-graded Serre spectral sequence. Homology Homotopy Appl. 12 (2010), no. 1, 75--92. https://projecteuclid.org/euclid.hha/1296223823