On the Homotopy Type of the Fredholm Lagrangian Grassmannian
José Carlos Corrêa Eidam, Paolo Piccione
Abstract
In 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.
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