Algebraic & Geometric Topology

On a spectral sequence for the cohomology of infinite loop spaces

Rune Haugseng and Haynes Miller

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Abstract

We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield–Kan cosimplicial space giving the 2–nilpotent completion of a connective spectrum X. Under good conditions its E2–term is computable as certain nonabelian derived functors evaluated at H(X) as a module over the Steenrod algebra, and it converges to the cohomology of ΩX. We provide general methods for computing the E2–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 E2 when X is a suspension spectrum.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2911-2947.

Dates
Received: 13 August 2015
Revised: 23 February 2016
Accepted: 7 March 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841234

Digital Object Identifier
doi:10.2140/agt.2016.16.2911

Mathematical Reviews number (MathSciNet)
MR3572354

Zentralblatt MATH identifier
1360.18024

Subjects
Primary: 18G40: Spectral sequences, hypercohomology [See also 55Txx] 55P47: Infinite loop spaces

Keywords
cohomology infinite loop spaces spectral sequence

Citation

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


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