English

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

R2 v1 2026-06-21T11:21:31.216Z