"Looped" principal connections and applications to loop space geometry

This talk reports on joint work with Mauro Spera. Given a principal bundle with connection one can define the induced "looped connection" on the looped principal bundle. We explain this procedure and apply it to the construction of Spin-c connections on the loop space of a finite-dimensional string manifold, and to show that the loop space of an arbitrary finite-dimensional manifold possesses a good cover in the sense of Leray.