Simply Connected 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...

The Classification of Simply Connected Manifolds of Positive Scalar Curvature

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Simply Connected Manifolds with Infinitely Many Toric Contact Structures and Constant Scalar Curvature Sasaki Metrics

We study a class of simply connected manifolds in all odd dimensions greater than 3 that exhibit an infinite number of toric contact structures of Reeb type that are inequivalent as contact structures. We compute the cohomology ring of our manifolds by using the join construction for Sasaki manifolds and show that all such contact structures admit a ray of compatible Sasaki metrics of constant ...

Arithmetic Manifolds of Positive Scalar Curvature

On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.