Differential geometry
Index of projective elliptic operators
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1230-1235.

Mathai, Melrose, and Singer introduced the notion of projective elliptic operators on manifolds equipped with an Azumaya bundle. In this note, we compute the equivariant index of transversally elliptic operators that are the pullback of projective elliptic operators on the trivialization of the Azumaya bundle. It encompasses the fractional index formula of projective elliptic operator by Mathai–Melrose–Singer.

Mathai, Melrose, et Singer ont introduit la notion d'opérateur elliptique projectif sur des variétés équipées d'un fibré d'Azumaya. Dans cette note, nous calculons les indices équivariants des opérateurs transversalement elliptiques qui s'obtiennent comme les tirés en arrière d'opérateurs elliptiques projectifs sur la variété qui trivialise le fibré d'Azumaya. Ces calculs généralisent la formule cohomologique de l'indice fractionnaire obtenue par Mathai–Melrose–Singer.

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DOI: 10.1016/j.crma.2016.10.018
Paradan, Paul-Émile 1

1 IMAG, UMR CNRS 5149, Université de Montpellier, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
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Paradan, Paul-Émile. Index of projective elliptic operators. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1230-1235. doi : 10.1016/j.crma.2016.10.018. http://www.numdam.org/articles/10.1016/j.crma.2016.10.018/

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