arXiv subjects

Gérald Gaudens

Publications and source records attributed to Gérald Gaudens.

6 recordsLinked to original sources

arXiv2015

Around conjectures of N. Kuhn

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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arXiv2013

An Operator model for connective K-theory with reality

We construct an explicit model for the connective cover of the spectrum of $K$-theory with reality. This model is a $\ztwo$-equivariant commutative symmetric ring spectrum which identifies with another one due to D. Dugger.

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arXiv2013

Relations in the modulo 2 homology of framed disks algebras

We study the homology structure of spaces having an action of the \emph{framed disks} operad. In particular, we compute the relations between Kudo-Araki operations and generalized Batalin-Vilkovisky operators. As an application, we complete the computations of the modulo 2 homology of $Ω^2 S^3$ as a Batalin-Vilkovisky algebra, and give some evidence for a classical conjecture about the modulo 2 Hurewicz homomorphism of the infinite loop space of the sphere spectrum.

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arXiv2010

Applications depuis K(Z/p,2) et une conjecture de Kuhn

On démontre une conjecture due á N. Kuhn concernant la cohomologie singuliére á coefficients mod p des espaces, comme module instable sur l'algébre de Steenrod. Notre démonstration de ce résultat, déjá connu en caractéristique 2, fait appel á une m'ethode nouvelle, qui fonctionne en toute caracteristique. De cette maniére on rétablit un r'esultat de [S98] dont la preuve est incompléte dans le cas d'un nombre premier impair. ---- We settle a conjecture due to N. Kuhn about the mod p cohomology of spaces considered as unstable modules over the Steenrod algebra. This result is already known to hold in characteristic 2. The method presented here is essentially new and works for all characteristics. In doing so we fix a gap in [S98] concerning the odd prime case.

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arXiv2010

Applications depuis K(Z/p, 2) et une conjecture de N. Kuhn

On démontre une conjecture due à N. Kuhn concernant la cohomologie singulière à coefficients mod p des espaces, comme module instable sur l'algèbre de Steenrod. Notre démonstration de ce résultat, déjà connu en caractéristique 2, fait appel à une méthode nouvelle, qui fonctionne en toute caractéristique. De cette manière on rétablit le résultat de [S98] dont la preuve est incomplète dans le cas d'un nombre premier impair. We settle a conjecture due to N. Kuhn about the mod p cohomology of spaces considered as unstable modules over the Steenrod algebra. This result is already known to hold in characteristic 2. The method presented here is essentially new and works for all characteristics. In doing so we fix a gap in [S98] concerning the odd prime case.

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arXiv2009

The $Γ$-structure of an additive track category

We prove that an additive track category with strong coproducts is equivalent to the category of pseudomodels for the algebraic theory of $\nil_2$ groups. This generalizes the classical statement that the category of models for the algebraic theory of abelian groups is equivalent to the category of abelian groups. Dual statements are also considered.

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