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2016 On a spectral sequence for the cohomology of infinite loop spaces
Rune Haugseng, Haynes Miller
Algebr. Geom. Topol. 16(5): 2911-2947 (2016). DOI: 10.2140/agt.2016.16.2911


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.


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Rune Haugseng. Haynes Miller. "On a spectral sequence for the cohomology of infinite loop spaces." Algebr. Geom. Topol. 16 (5) 2911 - 2947, 2016.


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

zbMATH: 1360.18024
MathSciNet: MR3572354
Digital Object Identifier: 10.2140/agt.2016.16.2911

Primary: 18G40, 55P47

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 5 • 2016
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