Metrics of positive scalar curvature Seminar

Given a manifold M, which admits a metric of positive scalar curvature:
how complicated is the space of all such metrics. Perhaps even more
significantly: how complicated is the moduli space of such metrics?
It has been known for quite a while that these spaces often have
infinitely many components. However, some people conjectured that the
components of the moduli space have no interesting structure, i.e. are
contractible.

We show that this is far from being the case: we construct elements in
homotopy groups of arbitrary high degree. We use index theory of the
Dirac operator to distinguish them.

In the talk, we will focus on some of the constructions of these
homotopy classes and on the method to show their non-triviality.