The equivariant Serre spectral sequence as an application of a spectral sequence of Spanier

✍ Scribed by Hannu Honkasalo

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 560 KB
• Volume: 90
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00180-6

✦ Synopsis

E.H. has constructed, for a cohomology theory defined on a triangulated space and locally constant on each open simplex, a spectral sequence whose &-term consists of certain simplicial cohomology groups, converging to the cohomology of the space. In this paper we study a closed G-fibration f : Y -+ X, where G is a finite group. We show that if the base-G-space X is equivariantly triangulated and Y is paracompact, then Spanier's spectral sequence yields an equivariant Serre spectral sequence for f. The main point here is to identify the equivariant singular cohomology groups of X with appropriate simplicial cohomology groups of the orbit space X/G.