Mass endomorphism, surgery and perturbations

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

1 UNIVERSITAET REGENSBURG - Universitaet Regensburg
2 KTH STOCKHOLM - Institutionen för Matematik - KTH
3 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: surgery; Dirac operator; mass endomorphism

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Mattias Dahl, Andreas Hermann, Emmanuel Humbert. Mass endomorphism, surgery and perturbations. Annales de l'Institut Fourier, 2014, 64 (2), pp.467-487. ⟨10.5802/aif.2855⟩. ⟨hal-00521700⟩