Exotic spheres and the Whitehead space

Framed Bordism and Lagrangian Embeddings of Exotic Spheres

Contents 1. Introduction 1 2. Construction of the bounding manifold 3 3. Transversality 21 4. Preliminaries for gluing 28 5. Construction of an extended gluing map 37 6. Local injectivity of the gluing map 52 7. Gluing near higher codimension strata 61 8. Construction of a smooth manifold with corners 74 9. Triviality of the tangent space of the cobordism 80 Appendix A. Pointwise estimates 88 A...

Exotic Spheres and Curvature

Since their discovery by Milnor in 1956, exotic spheres have provided a fascinating object of study for geometers. In this article we survey what is known about the curvature of exotic spheres.

Curvature and Symmetry of Milnor Spheres

Since Milnor’s discovery of exotic spheres [Mi], one of the most intriguing problems in Riemannian geometry has been whether there are exotic spheres with positive curvature. It is well known that there are exotic spheres that do not even admit metrics with positive scalar curvature [Hi] . On the other hand, there are many examples of exotic spheres with positive Ricci curvature (cf. [Ch1], [He...

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...

On Fibering Spheres by Toruses