H-space and loop space structures for intermediate curvatures

Abstract

For dimensions [Formula: see text] and [Formula: see text], we show that the space of metrics of [Formula: see text]-positive Ricci curvature on the sphere [Formula: see text] has the structure of an [Formula: see text]-space with a homotopy commutative, homotopy associative product operation. We further show, using the theory of operads and results of Boardman, Vogt and May, that the path component of this space containing the round metric is weakly homotopy equivalent to an [Formula: see text]-fold loop space.