On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifolds

The Seiberg-witten Equations on End-periodic Manifolds and Positive Scalar Curvature Metrics

By studying the Seiberg-Witten equations on end-periodic manifolds, we give an obstruction on the existence of positive scalar curvature metric on compact 4-manifolds with the same homology as S ˆ S. This obstruction is given in terms of the relation between the Frøyshov invariant of the generator of H3pX;Zq with the 4-dimensional Casson invariant λSW pXq defined in [6]. Along the way, we devel...

The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich’s eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

Arithmetic Manifolds of Positive Scalar Curvature

Simply Connected Manifolds of Positive Scalar Curvature

Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...

On the Scalar Curvature of Einstein Manifolds

We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.