2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74289In this article, we show that the Fredholm Lagrangian Grassmannian is homotopy equivalent with the space of compact perturbations of a fixed lagrangian. As a corollary, we obtain that the Maslov index with respect to a lagrangian is a isomorphism between the fundamental group of the Fredholm Lagrangian Grassmannian and the integers.Algebraic Topology58B05; 58B15text