2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75090We 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 figuresDifferential GeometryAlgebraic Topology58B20 (Primary); 58D15, 53C15 (Secondary)text