Boyer 9423752 Earlier the proposers discovered a class of 3-Sasakian manifolds; in the process gave explicit examples of simply connected strongly inhomogeneous Einstein manifolds of positive scalar curvature. The proposed problem here is to classify, topologically and differentiably, the aforementioned compact simply connected 3-Sasakian manifolds. They also studied the topology of the space of based holomorphic maps from the Riemann sphere to a complex flag manifold, motivated by the instanton moduli work of Segal; gave a stability theorem. This led to their solutions (Boyer and Mann in collaboration with Hurtubise and Milgram) of the Atiyah-Jones conjecture. They propose to extend the scope of the stability (and rationality) theorem to include certain almost homogeneous target spaces other than the flag manifolds. The proposed research is in the interface of differential topology and differential geometry; it may lay a mathematical foundation for parts of gauge theories, which serve as theoretical models for various unified field theories, in mathematical and theoretical physics.
