Around conjectures of N. Kuhn

Nguyen The Cuong; Gérald Gaudens; Geoffrey Powell; Lionel Schwartz

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arXiv · 1402.2617

Around conjectures of N. Kuhn

Nguyen The Cuong·Gérald Gaudens·Geoffrey Powell·Lionel Schwartz

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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 $\Fp$-vector spaces. The second result in particular exhibits the power of the functorial approach.

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BibTeX RIS

Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz. 2014-02-11. Around conjectures of N. Kuhn. https://arxiv.org/abs/1402.2617

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