The co-Riemannian Structure of Smooth Loop Spaces
arXiv:0809.3108
Abstract
We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a string manifold is a per-Hilbert-Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.
30 pages. Together with arXiv:0809.3401 this replaces math.DG/0505077