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