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

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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

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Differential Geometry, Algebraic Topology, 58B20 (Primary); 58D15, 53C15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/75090

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505077
 http://arxiv.org/abs/math/0505077

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arXiv