Mass endomorphism, surgery and perturbations
Annales de l'Institut Fourier, Volume 64 (2014) no. 2, p. 467-487

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.

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.

DOI : https://doi.org/10.5802/aif.2855
Classification:  53C27,  57R65,  58J05,  58J60
Keywords: Dirac operator, mass endomorphism, surgery.
@article{AIF_2014__64_2_467_0,
     author = {Ammann, Bernd and Dahl, Mattias and Hermann, Andreas and Humbert, Emmanuel},
     title = {Mass endomorphism, surgery and~perturbations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     pages = {467-487},
     doi = {10.5802/aif.2855},
     zbl = {1320.53053},
     mrnumber = {3330912},
     zbl = {06387282},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_2_467_0}
}
Ammann, Bernd; Dahl, Mattias; Hermann, Andreas; Humbert, Emmanuel. Mass endomorphism, surgery and perturbations. Annales de l'Institut Fourier, Volume 64 (2014) no. 2, pp. 467-487. doi : 10.5802/aif.2855. http://www.numdam.org/item/AIF_2014__64_2_467_0/

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