2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169389We 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/0505077Differential Geometry58B20 (Primary); 58D15, 53C15 (Secondary)text