The co-Riemannian Structure of Smooth Loop Spaces
Differential Geometry
2008-09-19 v1
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.
Keywords
Cite
@article{arxiv.0809.3108,
title = {The co-Riemannian Structure of Smooth Loop Spaces},
author = {Andrew Stacey},
journal= {arXiv preprint arXiv:0809.3108},
year = {2008}
}
Comments
30 pages. Together with arXiv:0809.3401 this replaces math.DG/0505077