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For dimensions n greater than or equal to 3, we show that the space ofmetrics of positive scalar curvature on the n-sphere is homotopy equivalent toa subspace which takes the form of a H-space with a homotopy commutative,homotopy associative product operation. This product operation is based on theconnected sum construction. We then exhibit an action of the little n-disksoperad on this subspace which, using results of Boardman, Vogt and May impliesthat when n=3 or n is at least 5, the space of metrics of positive scalarcurvature on the n-sphere is weakly homotopy equivalent to an n-fold loopspace.

H-Spaces, Loop Spaces and the Space of Positive Scalar Curvature Metrics on the Sphere