On the Homotopy Type of the Fredholm Lagrangian Grassmannian
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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