Title: Surgery and harmonic spinors (joint work with M. Dahl und E. Humbert)

Let M be a compact manifold with a fixed 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 its spin structure. We show that for generic metrics on M this bound is attained.