Mass endomorphism, surgery and perturbations

Ammann, Bernd; Dahl, Mattias; Hermann, Andreas; Humbert, Emmanuel

doi:10.5802/aif.2855

Mass endomorphism, surgery and perturbations
[Endomorphisme de masse, chirurgie et perturbations]

Ammann, Bernd ¹ ; Dahl, Mattias ² ; Hermann, Andreas ³ ; Humbert, Emmanuel ³

¹ Fakultät für Mathematik Universität Regensburg 93040 Regensburg Germany
² Institutionen för Matematik Kungliga Tekniska Högskolan 100 44 Stockholm Sweden
³ Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37200 Tours, France

Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 467-487.

Résumé
Abstract

Nous montrons que l’endomorphisme de masse associé à l’opérateur de Dirac sur une variété riemannienne est non nul pour une métrique générique. La preuve s’appuie sur l’étude du comportement par chirurgie de l’endomorphisme de masse, de son comportement au voisinage d’une métrique possédant des spineurs harmoniques et par des arguments de perturbations analytiques.

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

EuDML MR Zbl

DOI : 10.5802/aif.2855

Classification : 53C27, 57R65, 58J05, 58J60
Keywords: Dirac operator, mass endomorphism, surgery.
Mot clés : Opérateur de Dirac, endomorphisme de masse, chirurgie.

Affiliations des auteurs :

Ammann, Bernd ¹ ; Dahl, Mattias ² ; Hermann, Andreas ³ ; Humbert, Emmanuel ³

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     title = {Mass endomorphism, surgery and~perturbations},
     journal = {Annales de l'Institut Fourier},
     pages = {467--487},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     doi = {10.5802/aif.2855},
     mrnumber = {3330912},
     zbl = {1320.53053},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2855/}
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Ammann, Bernd; Dahl, Mattias; Hermann, Andreas; Humbert, Emmanuel. Mass endomorphism, surgery and perturbations. Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 467-487. doi : 10.5802/aif.2855. http://www.numdam.org/articles/10.5802/aif.2855/

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