Members & Former Members

The main result of this paper is that when M_0, M_1 are two simply connected spin manifolds of the same dimension d≥5 which both admit a metric of positive scalar curvature, the spaces \mathcal{M}^+(M0) and \mathcal{M}^+(M_1) of such metrics are homotopy equivalent. This supersedes a previous result of Chernysh and Walsh which gives the same conclusion when M_0 and M_1 are also spin cobordant.

We also prove an analogous result for simply connected manifolds which do not admit a spin structure; we need to assume that d≠8 in that case.

Related project(s):
15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds