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Comptes Rendus Mathématique
Volume 347, n° 23-24
pages 1393-1398 (décembre 2009)
Doi : 10.1016/j.crma.2009.10.021
Received : 6 May 2009 ;  accepted : 14 October 2009
An index theorem for manifolds with boundary
Un théorème d’indice pour des variétés à bord
 

Paulo Carrillo-Rouse , Bertrand Monthubert
Institut de mathématiques de Toulouse, université de Toulouse, 31062 Toulouse cedex 9, France 

Abstract

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  . Following these ideas, we prove an index theorem for manifolds with boundary. To cite this article: P. Carrillo-Rouse, B. Monthubert, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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

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  . Nous suivons ces idées pour montrer un théorème d’indice pour des variétés à bord. Pour citer cet article : P. Carrillo-Rouse, B. Monthubert, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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


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