An index theorem for manifolds with boundary

Paulo Carrillo-Rouse; Bertrand Monthubert

doi:10.1016/j.crma.2009.10.021

Geometry/Differential Topology

An index theorem for manifolds with boundary
[Un théorème d'indice pour des variétés à bord]

Présenté par : Alain Connes

Paulo Carrillo-Rouse ¹ ; Bertrand Monthubert ¹

¹ Institut de mathématiques de Toulouse, université de Toulouse, 31062 Toulouse cedex 9, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1393-1398.

Résumé
Abstract

Dans le livre Non Commutative Geometry, 1994, II.5, Connes donne une preuve du théorème de l'indice d'Atiyah–Singer pour des variétés fermées en utilisant des groupoïdes de déformation et des actions appropriées de ceux-ci dans $R^{N}$ . Nous suivons ces idées pour montrer un théorème d'indice pour des variétés à bord.

In Connes (Non Commutative Geometry, 1994, II.5), a proof is given of the Atiyah–Singer index theorem for closed manifolds by using deformation groupoids and appropriate actions of these on $R^{N}$ . Following these ideas, we prove an index theorem for manifolds with boundary.

Reçu le : 2009-05-06
Accepté le : 2009-10-14
Publié le : 2009-11-12

DOI : 10.1016/j.crma.2009.10.021

Affiliations des auteurs :

Paulo Carrillo-Rouse ¹ ; Bertrand Monthubert ¹

¹ Institut de mathématiques de Toulouse, université de Toulouse, 31062 Toulouse cedex 9, France

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     title = {An index theorem for manifolds with boundary},
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Paulo Carrillo-Rouse; Bertrand Monthubert. An index theorem for manifolds with boundary. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1393-1398. doi : 10.1016/j.crma.2009.10.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.021/

Bibliographie
Cité par

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[11] A. Paterson Groupoids, Inverse Semigroups, and their Operator Algebras, Progress in Mathematics, vol. 170, Birkhäuser Boston, Inc., Boston, MA, 1999 (xvi+274 pp)

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