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.
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.
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@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/
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