Surgery and Harmonic Spinors

Bernd Ammann (1) , Mattias Dahl (2) , Emmanuel Humbert (1)

1 IECN - Institut Élie Cartan de Nancy
2 KTH STOCKHOLM - Institutionen för Matematik - KTH

Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and \chi. We show that for generic metrics on M this bound is attained.

Mots clés: Dirac operator; eigenvalue; surgery

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Mattias Dahl, Emmanuel Humbert. Surgery and Harmonic Spinors. 2006. ⟨hal-00079157⟩