On non-realization results and conjectures of N. Kuhn

TitreOn non-realization results and conjectures of N. Kuhn
Type de publicationArticle de revue
AuteurCuong, Nguyen The, Gaudens, Gerald, Powell, Geoffrey , Schwartz, Lionel
PaysPologne
EditeurPolskiej Akademii Nauk, Instytut Matematyczny
VilleVarsovie
TypeArticle scientifique dans une revue à comité de lecture
Année2016
LangueAnglais
Date29 fév.2016
Numéro234
Pagination139–161
Titre de la revueFundamenta Mathematicae
ISSN1730-6329
Résumé en anglais

We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod-p singular cohomology of a space, for p a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes’ mapping space theorem. The second (for the prime 2) is based on an analysis of the -1 and -2 columns of the Eilenberg–Moore spectral sequence, and of the associated extension.

In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between Fp-vector spaces. The second result in particular exhibits the power of the functorial approach.

URL de la noticehttp://okina.univ-angers.fr/publications/ua14916
DOI10.4064/fm95-10-2015
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Titre abrégéFundam. Math.