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Comptes Rendus Mathématique
Volume 341, n° 12
pages 751-754 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.015
Received : 24 May 2005 ;  accepted : 11 October 2005
K -théorie pour les singularités coniques isolées
K -theory for conical isolated singularities

André Legrand , David Poutriquet
Laboratoire de mathématiques Emile-Picard, université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France 


Pour une variété singulière compacte à singularités coniques isolées, on construit des groupes de K -théorie paramétrés par un entier positif strictement inférieur à la dimension de la variété. Rationnellement cʼest le groupe de K -théorie de la variété pour lʼentier nul et pour la valeur maximum du paramètre cʼest celui de la variété à bord obtenue par excision des points singuliers. On construit aussi un caractère de Chern à valeurs dans la cohomologie dʼintersection pour une perversité convenable. Cʼest un isomorphisme dans le cadre rationnel. Une version « à la Chern-Weil » des constructions précédentes est obtenue en utilisant la K -théorie multiplicative de Karoubi. Pour citer cet article : A. Legrand, D. Poutriquet, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

For a compact singular variety with isolated conical singularities we define K -theory groups which depend upon a non-negative integer less than the dimension. In the rational setting, the null case gives the K -theory of the singular variety, the biggest case gives the K -theory of the manifold with boundary obtained when excising the singular points. We define also a Chern character which takes its values in the intersection cohomology associated to a suitable perversity. This character is an isomorphism in the rational setting. We give a Chern-Weil version of the above constructions using the multiplicative K -theory of Karoubi. To cite this article: A. Legrand, D. Poutriquet, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

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