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

2013/01/23 by Walsh, Mark · 2 citations
#53C99 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.5670

Abstract

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.

Cited by

• Finite extinction time of a family of homogeneous Ricci flows
• Classification of spin^c manifolds with generalized positive scalar curvature

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