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Sur une application possible du concept d’homotopie à la théorie des modèles

Brice Halimi (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

Cet article vise à appliquer certains concepts de la théorie moderne de l’homotopie à la théorie des modèles. En particulier, le concept d’ensemble simplicial est employé pour décrire les formules d’un langage L du premier ordre, les ensembles définissables d’une structure d’interprétation de L, et les espaces de types d’une théorie couchée dans L. On montre qu’à toute structure d’interprétation de L peut être associé un ensemble simplicial, selon une correspondance fonctorielle qui traduit plongements...

Surgery on pairs of closed manifolds

Alberto Cavicchioli, Yuri V. Muranov, Fulvia Spaggiari (2009)

Czechoslovak Mathematical Journal

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group L P * generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the...

Survey of Oka theory.

Forstnerič, Franc, Lárusson, Finnur (2011)

The New York Journal of Mathematics [electronic only]

Symplectic groups are N-determined 2-compact groups

Aleš Vavpetič, Antonio Viruel (2006)

Fundamenta Mathematicae

We show that for n ≥ 3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus.

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