# A Quick View of Lagrangian Floer Homology

## TL;DR

This paper provides an accessible overview of Lagrangian Floer homology, its foundational concepts in symplectic geometry, and its role in addressing Arnol'd's conjecture on fixed points of Hamiltonian diffeomorphisms.

## Contribution

It offers a concise introduction connecting Floer homology with symplectic geometry and the Arnol'd conjecture, highlighting key ideas and their interrelations.

## Key findings

- Explains the basics of Morse theory and critical points.
- Introduces symplectic geometry concepts relevant to Floer homology.
- Describes the connection between Floer homology and Arnol'd's conjecture.

## Abstract

In this note we present a brief introduction to Lagrangian Floer homology and its relation with the solution of Arnol'd conjecture, on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism. We start with the basic definition of critical point on smooth manifolds, in oder 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 Arnol'd Conjecture and how is related to the intersection of Lagrangian submanifolds.