On the Homotopy Type of the Fredholm Lagrangian Grassmannian

2005/02/23 by José Carlos Corrêa Eidam, Paolo Piccione, Eidam, José Carlos Corrêa +1
Mathematics · #58B05 #58B15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AT #msc:58B05 #msc:58B15

paper · pdf · doi:10.48550/arxiv.math/0502480

openalex publication_date 2005/02/23 · arxiv created 2005/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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