Strongly positive curvature

Positive Ricci Curvature

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ the moduli space of Sasakian structures has infinitely many positive components det...

Positive Scalar Curvature

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4– manifolds. The vanishing of the Seiberg–Witten invariants of a manifold admitting such a metric may be viewed as a non-linear generalization of the classic conditions [12, 11] derived from the Dirac operator. If a manifo...

of non-positive Gaussian curvature

Positive Scalar Curvature and Surgery

Positive Scalar Curvature with Symmetry

We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S-manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following generalization of a resu...