Mattias Dahl: D-minimal metrics on compact spin manifolds.

On a compact connected spin manifold the index theorem by Atiyah and Singer gives lower bounds for the dimension of the kernel of the Dirac operator. Metrics for which the lower bound is attained are called D-minimal. It is known that generic metrics are D-minimal and that non-D-minimal metrics exist on many manifolds. In this talk, I will discuss these older results. I will also present new results on the connectedness of the space of D-minimal metrics (joint work with Bernd Ammann, Regensburg).