On a spectral sequence for the cohomology of infinite loop spaces
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Author(s)
Haugseng, Rune Gjoringbo
Miller, Haynes R
Date Issued
November 2016
Journal
Algebraic & Geometric Topology
Publisher
Mathematical Sciences Publishers
Citation
Haugseng, Rune, and Haynes Miller. “On a Spectral Sequence for the Cohomology of Infinite Loop Spaces.” Algebraic & Geometric Topology 16, 5 (November 2016): 2911–2947 © 2016 Mathematical Sciences Publishers
Version
Original manuscript
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 Ω ∞ X. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2140/AGT.2016.16.2911
