Resumen de Surgery and harmonic spinors

Bernd Ammann, Mattias Dahl, Emmanuel Humbert

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