Contractibility of spaces of positive scalar curvature metrics with symmetry

21.08.2025, 16:15  –  Raum 0.12
Forschungsseminar Differentialgeometrie

Bernhard Hanke (Augsburg)

Spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds have been studied intensively for many years. Typically, these spaces, if non-empty, are topologically highly non-trivial. However, the situation changes drastically under symmetry assumptions. In this talk, we demonstrate the contractibility of spaces of invariant metrics of positive scalar curvature on closed, connected manifolds with S¹-actions containing fixed-point components of codimension two. 

Key ingredients are the local flexibility properties of positive scalar curvature metrics and the smoothing of mean-convex singularities. 

This is joint work with Christian Bär.