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.
Keywords: Dirac operator, mass endomorphism, surgery.
Mot clés : Opérateur de Dirac, endomorphisme de masse, chirurgie.
Ammann, Bernd 1; Dahl, Mattias 2; Hermann, Andreas 3; Humbert, Emmanuel 3
@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}, pages = {467--487}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {2}, year = {2014}, doi = {10.5802/aif.2855}, zbl = {1320.53053}, mrnumber = {3330912}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2855/} }
TY - JOUR AU - Ammann, Bernd AU - Dahl, Mattias AU - Hermann, Andreas AU - Humbert, Emmanuel TI - Mass endomorphism, surgery and perturbations JO - Annales de l'Institut Fourier PY - 2014 SP - 467 EP - 487 VL - 64 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2855/ DO - 10.5802/aif.2855 LA - en ID - AIF_2014__64_2_467_0 ER -
%0 Journal Article %A Ammann, Bernd %A Dahl, Mattias %A Hermann, Andreas %A Humbert, Emmanuel %T Mass endomorphism, surgery and perturbations %J Annales de l'Institut Fourier %D 2014 %P 467-487 %V 64 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2855/ %R 10.5802/aif.2855 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2855/
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