The co-Riemannian Structure of Smooth Loop Spaces

Andrew Stacey

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arXiv · 0809.3108

The co-Riemannian Structure of Smooth Loop Spaces

Andrew Stacey

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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.

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Andrew Stacey. 2008-09-18. The co-Riemannian Structure of Smooth Loop Spaces. https://arxiv.org/abs/0809.3108

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