Boris Botvinnik, University of Oregon

Title: Spin^c manifolds, positive scalar curvature and manifolds with fibered singularities.

Abstract: I will discuss a problem of existence of positive scalar curvature on manifolds with fibered singularities. It turns out there are necessary and sufficient conditions for a psc-metric to exist on such objects. There is a particular case of manifolds with fibered singularities when the fiber is a circle. This case leads to psc-metrics spin^c manifolds with special conditions near the singular locus. In particular, I describe some results concerning metrics on spin^c manifolds with positive ``twisted scalar curvature,'' where the twisting comes from the curvature of the spin^c line bundle.

This work is joint with Jonathan Rosenberg.