How to Construct a Dirac Operator in Infinite Dimensions

Abstract

We define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this approach works for the smooth loop space of a so-called string manifold.

10 pages. Together with arXiv:0809.3108 this replaces math.DG/0505077

References in corpus (1)

• The co-Riemannian Structure of Smooth Loop Spaces

Cited by in corpus (2)

• An introduction to infinite-dimensional differential geometry
• The co-Riemannian Structure of Smooth Loop Spaces