Elliptic operators and higher signatures

Leichtnam, Éric; Piazza, Paolo

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

Annales de l'Institut Fourier, Tome 54 (2004), p. 1197-1277 / Harvested from Numdam

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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.

Publié le : 2004-01-01

MR 2127848 | Zbl 1069.58014 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2049
Classification: 19E20, 53C05, 58J05, 58J28

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     volume = {54},
     year = {2004},
     pages = {1197-1277},
     doi = {10.5802/aif.2049},
     mrnumber = {2127848},
     zbl = {1069.58014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_5_1197_0}
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Leichtnam, Éric; Piazza, Paolo. Elliptic operators and higher signatures. Annales de l'Institut Fourier, Tome 54 (2004) pp. 1197-1277. doi : 10.5802/aif.2049. http://gdmltest.u-ga.fr/item/AIF_2004__54_5_1197_0/

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