Sasakian geometry, hypersurface singularities, and Einstein metrics
Einstein metrics on exotic spheres in dimensions 7, 11 and 15.
Einstein manifolds of positive scalar curvature with arbitrary second Betti number.
Einstein metrics on rational homology 7-spheres
In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2- connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.
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