# ANNALES DE L'INSTITUT FOURIER

Elliptic operators and higher signatures
Annales de l'Institut Fourier, Volume 54 (2004) no. 5, pp. 1197-1277.

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.

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.

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, Volume 54 (2004) no. 5, pp. 1197-1277. doi : 10.5802/aif.2049. https://aif.centre-mersenne.org/articles/10.5802/aif.2049/

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