Universität Augsburg
Institut für Mathematik

We show the contractibility of spaces of invariant Riemannian metrics of positive scalar curvature on compact connected manifolds of dimension at least two with and without boundary and equipped with compact Lie group actions. On manifolds without boundary, we assume that the Lie group contains a normal S^1-subgroup with fixed-point components of codimension two. In this situation, Wiemeler has shown previously that invariant metrics of positive scalar curvature exist.

For the proof, we combine equivariant Morse theory with conformal deformations near unstable manifolds. On manifolds without boundary, we also use local flexibility properties of positive scalar curvature metrics and the smoothing of mean-convex singularities.

This is joint work with Christian Bär.