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arXiv · 1505.02432

Essential extensions, the nilpotent filtration and the Arone-Goodwillie tower

Geoffrey Powell
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Abstract

The spectral sequence associated to the Arone-Goodwillie tower for the n-fold loop space functor is used to show that the first two non-trivial layers of the nilpotent filtration of the reduced mod 2 cohomology of a (sufficiently connected) space with nilpotent cohomology are comparable. This relies upon the theory of unstable modules over the mod 2 Steenrod algebra, together with properties of a generalized class of almost unstable modules which is introduced here. An essential ingredient of the proof is a non-vanishing result for certain extension groups in the category of unstable modules localized away from nilpotents.

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BibTeXRIS

Geoffrey Powell. 2015-05-10. Essential extensions, the nilpotent filtration and the Arone-Goodwillie tower. https://doi.org/10.1112/jlms%2Fjdw026

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