Elliptic operators and higher signatures  [ Opérateurs elliptiques et hautes signatures ]
Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1197-1277.

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.

DOI : https://doi.org/10.5802/aif.2049
Classification : 19E20,  53C05,  58J05,  58J28
Mots clés: opérateurs elliptiques, problèmes aux bords, théorie de l’indice, invariants éta, hautes signatures de Novikov, invariance par homotopie, invariance par coupure et collage
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     author = {Leichtnam, Eric and Piazza, Paolo},
     title = {Elliptic operators and higher signatures},
     journal = {Annales de l'Institut Fourier},
     pages = {1197--1277},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     doi = {10.5802/aif.2049},
     zbl = {1069.58014},
     mrnumber = {2127848},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2004__54_5_1197_0/}
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Leichtnam, Eric; 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. https://aif.centre-mersenne.org/item/AIF_2004__54_5_1197_0/

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