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.

Type de document :
Article dans une revue
Journal of the London Mathematical Society, London Mathematical Society, 2016, 94 (1), pp.85-112. 〈http://jlms.oxfordjournals.org/content/94/1/85〉. 〈10.1112/jlms/jdw026〉
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https://hal.archives-ouvertes.fr/hal-01392730
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 4 novembre 2016 - 16:25:01
Dernière modification le : lundi 5 février 2018 - 15:00:03

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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. 〈http://jlms.oxfordjournals.org/content/94/1/85〉. 〈10.1112/jlms/jdw026〉. 〈hal-01392730〉

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