[Un théorème d'indice pour des variétés à bord]
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.
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.
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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, Tome 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] 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] Non Commutative Geometry, Academic Press, Inc., San Diego, CA, 1994
[3] K-duality for pseudomanifolds with isolated singularities, J. Funct. Anal., Volume 219 (2005), pp. 109-133
[4] Groupoids and an index theorem for conical pseudomanifolds, J. Reine Angew. Math., Volume 628 (2009), pp. 1-35
[5] Pseudodifferential analysis on continuous family groupoids, Doc. Math., Volume 5 (2000), pp. 625-656
[6] 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] Introduction to Foliations and Lie Groupoids, Cambridge Studies in Advanced Mathematics, vol. 91, 2003
[8] Groupoids and pseudodifferential calculus on manifolds with corners, J. Funct. Anal., Volume 199 (2003) no. I, pp. 243-286
[9] Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris Sér. I, Volume 325 (1997), pp. 193-198
[10] 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] 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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