On a spectral sequence for the cohomology of infinite loop spaces

Haugseng, Rune¹ ; Miller, Haynes²

¹Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
²Department of Mathematics, Massachusetts Institute of Technology, Building 2, Room 106, %Rm 2-237 this seems to be old office number 77 Massachusetts Avenue, Cambridge, MA 02139-4307, United States

Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2911-2947

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.2911

Classification : 18G40, 55P47
Keywords: cohomology, infinite loop spaces, spectral sequence

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