Around conjectures of N. Kuhn

Nguyen The Cuong (1) , Gérald Gaudens (2) , Geoffrey Powell (2) , Lionel Schwartz (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: extensions; Unstable modules and algebras; indecomposables; Eilenberg-Moore spectral sequence

Domaines: Topologie algébrique [math.AT]

Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz. Around conjectures of N. Kuhn. 2014. ⟨hal-00944820v2⟩