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On non-realization results and conjectures of N. Kuhn

Volume 234 / 2016

Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz Fundamenta Mathematicae 234 (2016), 139-161 MSC: Primary 55S10; Secondary 55S35. DOI: 10.4064/fm95-10-2015 Published online: 29 February 2016

Abstract

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 ${\mathbb F}_p$-vector spaces. The second result in particular exhibits the power of the functorial approach.

Authors

  • Nguyen The CuongLIA CNRS Formath Vietnam
    and
    Université Paris 13
    93430 Villetaneuse, France
    e-mail
  • Gérald GaudensLAREMA, UMR 6093 CNRS
    and
    Université d’Angers
    49045 Angers, France
    e-mail
  • Geoffrey PowellLAREMA, UMR 6093 CNRS
    and
    Université d’Angers
    49045 Angers, France
    e-mail
  • Lionel SchwartzLAGA, UMR 7539 CNRS
    and
    Université Paris 13
    93430 Villetaneuse, France
    e-mail

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