Geometry/Differential Topology
An index theorem for manifolds with boundary
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1393-1398.

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 RN. Following these ideas, we prove an index theorem for manifolds with boundary.

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 RN. Nous suivons ces idées pour montrer un théorème d'indice pour des variétés à bord.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.10.021
Carrillo-Rouse, Paulo 1; Monthubert, Bertrand 1

1 Institut de mathématiques de Toulouse, université de Toulouse, 31062 Toulouse cedex 9, France
@article{CRMATH_2009__347_23-24_1393_0,
     author = {Carrillo-Rouse, Paulo and Monthubert, Bertrand},
     title = {An index theorem for manifolds with boundary},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1393--1398},
     publisher = {Elsevier},
     volume = {347},
     number = {23-24},
     year = {2009},
     doi = {10.1016/j.crma.2009.10.021},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.021/}
}
TY  - JOUR
AU  - Carrillo-Rouse, Paulo
AU  - Monthubert, Bertrand
TI  - An index theorem for manifolds with boundary
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1393
EP  - 1398
VL  - 347
IS  - 23-24
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.10.021/
DO  - 10.1016/j.crma.2009.10.021
LA  - en
ID  - CRMATH_2009__347_23-24_1393_0
ER  - 
%0 Journal Article
%A Carrillo-Rouse, Paulo
%A Monthubert, Bertrand
%T An index theorem for manifolds with boundary
%J Comptes Rendus. Mathématique
%D 2009
%P 1393-1398
%V 347
%N 23-24
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.10.021/
%R 10.1016/j.crma.2009.10.021
%G en
%F CRMATH_2009__347_23-24_1393_0
Carrillo-Rouse, Paulo; Monthubert, Bertrand. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.10.021/

[1] Carrillo-Rouse, P. A Schwartz type algebra for the tangent groupoid, K-theory and Noncommutative Geometry, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2008, pp. 181-199

[2] Connes, A. Non Commutative Geometry, Academic Press, Inc., San Diego, CA, 1994

[3] Debord, C.; Lescure, J.M. K-duality for pseudomanifolds with isolated singularities, J. Funct. Anal., Volume 219 (2005), pp. 109-133

[4] Debord, C.; Lescure, J.M.; Nistor, V. Groupoids and an index theorem for conical pseudomanifolds, J. Reine Angew. Math., Volume 628 (2009), pp. 1-35

[5] Lauter, R.; Monthubert, B.; Nistor, V. Pseudodifferential analysis on continuous family groupoids, Doc. Math., Volume 5 (2000), pp. 625-656

[6] Melrose, R. The Atiyah–Patodi–Singer Index Theorem, Research Notes in Mathematics, vol. 4, A K Peters, Ltd., Wellesley, MA, 1993 xiv+377 pp. (English summary)

[7] Moerdijk, I.; Mrčun, J. Introduction to Foliations and Lie Groupoids, Cambridge Studies in Advanced Mathematics, vol. 91, 2003

[8] Monthubert, B. Groupoids and pseudodifferential calculus on manifolds with corners, J. Funct. Anal., Volume 199 (2003) no. I, pp. 243-286

[9] Monthubert, B.; Pierrot, F. Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris Sér. I, Volume 325 (1997), pp. 193-198

[10] Monthubert, B. Contribution of noncommutative geometry to index theory on singular manifolds, Geometry and Topology of Manifolds, Banach Center Publ., vol. 76, Polish Acad. Sci., Warsaw, 2007, pp. 221-237

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

Cited by Sources: