Charles P. Boyer, Krzysztof Galicki, János Kollár, Evan Thomas
Published 2003-11-17Version 1
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 $4m-1, m\geq2$ admit Sasakian-Einstein metrics \cite{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 $7.$
Comments: 7 pages
Journal: Experimental Mathematics 14 (2005), 61-66.
On the moduli space of positive Ricci curvature metrics on homotopy spheres
Moduli spaces of nonnegatively curved metrics on exotic spheres
Highly connected 7-manifolds and non-negative curvature
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