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A Quick View of Lagrangian Floer Homology

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Geometrical Themes Inspired by the N-body Problem

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2204))

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Abstract

In this note we present a brief introduction to Lagrangian Floer homology and its relation to the solution to the Arnol’d Conjecture, on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism. We start with the basic definition of a critical point on smooth manifolds, in order to sketch some aspects of Morse theory. Introduction to the basics concepts of symplectic geometry are also included with the idea of understanding the statement of the Arnol’d Conjecture and how it is related to the intersection of Lagrangian submanifolds.

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Authors and Affiliations

  1. Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340, 28045, Colima, Colima, Mexico

    Andrés Pedroza

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  1. Andrés Pedroza
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Correspondence to Andrés Pedroza .

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Editors and Affiliations

  1. Department of Mathematics, Mathematics Research Center (CIMAT), Guanajuato, Mexico

    Luis Hernández-Lamoneda

  2. Department of Mathematics, Rutgers University, Camden, NJ, USA

    Haydeé Herrera

  3. Department of Mathematics, Mathematics Research Center (CIMAT), Guanajuato, Mexico

    Rafael Herrera

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Pedroza, A. (2018). A Quick View of Lagrangian Floer Homology. In: Hernández-Lamoneda, L., Herrera, H., Herrera, R. (eds) Geometrical Themes Inspired by the N-body Problem. Lecture Notes in Mathematics, vol 2204. Springer, Cham. https://doi.org/10.1007/978-3-319-71428-8_3

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