On non-realization results and conjectures of N. Kuhn

• Autorzy: Nguyen The Cuong , Gérald Gaudens , Geoffrey Powell , Lionel Schwartz
• Języki publikacji: EN

Abstrakty

EN

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 $𝔽_{p}$-vector spaces. The second result in particular exhibits the power of the functorial approach.

Kategorie tematyczne

• 55S35: Obstruction theory
• 55S10: Steenrod algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 234
• Numer: 2
• Strony: 139-161

Daty

wydano

2016

Twórcy

autor

Nguyen The Cuong

• LIA CNRS Formath Vietnam
• Université Paris 13, 93430 Villetaneuse, France

autor

Gérald Gaudens

• LAREMA, UMR 6093 CNRS
• Université d'Angers, 49045 Angers, France

autor

Geoffrey Powell

• LAREMA, UMR 6093 CNRS
• Université d'Angers, 49045 Angers, France

autor

Lionel Schwartz

• LAGA, UMR 7539 CNRS
• Université Paris 13, 93430 Villetaneuse, France

Identyfikatory

DOI

10.4064/fm95-10-2015