On the Homotopy Type of the Fredholm Lagrangian Grassmannian

Details On the Homotopy Type of the Fredholm Lagrangian Grassmannian On the Homotopy Type of the Fredholm Lagrangian Grassmannian

2005-02-23

arxiv.org/abs/math/0502480v2

Mathematics

Algebraic Topology

Scientific paper

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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