Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15
Abstract
In a recent article the first three authors proved that in dimension 4m+1 all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension 4m-1, m≥2 admit Sasakian-Einstein metrics BGK, and proved this for the simplest case, namely dimension 7. In this paper we describe computer programs that show that this conjecture is also true for 11-spheres and 15-spheres. Moreover, a program is given that determines the partition of the 8610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension 7.
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