On non-realization results and conjectures of N. Kuhn
Volume 234 / 2016
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.
