# On a spectral sequence for the cohomology of infinite loop spaces

@article{Haugseng2016OnAS, title={On a spectral sequence for the cohomology of infinite loop spaces}, author={Rune Haugseng and Haynes R. Miller}, journal={Algebraic \& Geometric Topology}, year={2016}, volume={16}, pages={2911-2947} }

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 1 X . We provide general methods for computing the E2 ‐term, including the construction of a multiplicative spectral sequence of Serre type… Expand

#### 3 Citations

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Working over the prime field of characteristic two, consequences of the Koszul duality between the Steenrod algebra and the big Dyer-Lashof algebra are studied, with an emphasis on the interplay… Expand

On the Derived Functors of Destabilization and of Iterated Loop Functors

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These notes explain how to construct small functorial chain complexes which calculate the derived functors of destabilization (respectively iterated loop functors) in the theory of modules over the… Expand

Andr\'{e}-Quillen homology of spectral Lie algebras with application to mod p homology of labeled configuration spaces

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We provide a general method to compute the mod 2 André-Quillen homology of spectral Lie algebras. This is the E-page of Knudsen’s spectral sequence, which converges to the mod 2 homology of… Expand

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