The Geometry of the Loop Space and a Construction of a Dirac Operator

Abstract

We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous to the Dirac operator of a spin manifold.

52 pages, no figures

Cited by in corpus (1)

• The differential topology of loop spaces