Elliptic operators and higher signatures

Leichtnam, Éric; Piazza, Paolo

doi:10.5802/aif.2049

Elliptic operators and higher signatures
[Opérateurs elliptiques et hautes signatures]

Leichtnam, Éric ; Piazza, Paolo

Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1197-1277.

Résumé
Abstract

En s'appuyant sur la théorie des opérateurs elliptiques, nous donnons une approche unifiée des sujets suivants : - le problème de l'invariance par homotopie des hautes signatures de Novikov des variétés compactes orientées sans bord, - le problème de l'invariance par coupure et collage des hautes signatures de Novikov des variétés compactes orientées sans bord, - le problème de définir les hautes signatures de variétés à bord et de prouver leur invariance par homotopie.

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2049

Classification : 19E20, 53C05, 58J05, 58J28

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Leichtnam, Éric; Piazza, Paolo. Elliptic operators and higher signatures. Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1197-1277. doi : 10.5802/aif.2049. http://www.numdam.org/articles/10.5802/aif.2049/

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