Moduli Spaces of Positive Curvature Metrics

Abstract:

Besides the space of positive scalar curvature metrics, various moduli spaces have gained a lot of attention. Among those, the observer moduli space arguably has the best behaviour from a homotopy-theoretical perspective because the subgroup of observer diffeomorphisms acts freely on the space of Riemannian metrics if the underlying manifold is connected.

In this talk, I will present how to construct non-trivial elements in the second homotopy of the observer moduli space of positive scalar curvature metrics for a large class for four-manifolds. I will further outline how to adapt this construction to produce the first non-trivial elements in higher homotopy groups of the observer moduli space of positive sectional curvature metrics on complex projective spaces.