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

Andrew Stacey

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

Andrew Stacey

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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.

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Andrew Stacey. 2005-05-04. The Geometry of the Loop Space and a Construction of a Dirac Operator. https://arxiv.org/abs/math/0505077

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