Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 5 (2016), 2911-2947.
On a spectral sequence for the cohomology of infinite loop spaces
We study the mod- cohomology spectral sequence arising from delooping the Bousfield–Kan cosimplicial space giving the –nilpotent completion of a connective spectrum . Under good conditions its –term is computable as certain nonabelian derived functors evaluated at as a module over the Steenrod algebra, and it converges to the cohomology of . We provide general methods for computing the –term, including the construction of a multiplicative spectral sequence of Serre type for cofibration sequences of simplicial commutative algebras. Some simple examples are also considered; in particular, we show that the spectral sequence collapses at when is a suspension spectrum.
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2911-2947.
Received: 13 August 2015
Revised: 23 February 2016
Accepted: 7 March 2016
First available in Project Euclid: 16 November 2017
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Haugseng, Rune; Miller, Haynes. On a spectral sequence for the cohomology of infinite loop spaces. Algebr. Geom. Topol. 16 (2016), no. 5, 2911--2947. doi:10.2140/agt.2016.16.2911. https://projecteuclid.org/euclid.agt/1510841234