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

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 important ingredient of the proof is a non-vanishing result for certain extension groups in the category of unstable modules modulo nilpotents.

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https://hal.archives-ouvertes.fr/hal-01392730
Contributor : Okina Université d'Angers <>
Submitted on : Friday, November 4, 2016 - 4:25:01 PM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM

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Geoffrey Powell. Essential extensions, the nilpotent filtration and the Arone–Goodwillie tower. Journal of the London Mathematical Society, London Mathematical Society, 2016, 94 (1), pp.85-112. ⟨10.1112/jlms/jdw026⟩. ⟨hal-01392730⟩

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