# Lagrangian Floer homology

This is a course for the second semester of M2 * (option géométrie). *
In the first half of the course we will study the basics of symplectic topology and Morse
theory, while the second half will concentrate on the more advanced topic of Lagrangian
Floer homology. This topics are a prerequisite for the advanced course
* Derived categories in symplectic geometry * by
Baptiste
Chantraine and Hossein
Abbaspour.
## Practical information

Classes meet on Monday from 9:30 to 12:00 in * Salle Hypatia. *

Office hours are in
office 109 of the * Laboratoire de mathématiques * on Wednesday from
14:00 to 15:30, or by appointment
(paolo.ghiggini@univ-nantes.fr).
## Topics

- Symplectic manifolds and Lagrangian submanifolds: definitions and examples
- Stability and local forms
- Liouville manifolds
- Morse homology
- Overview of Lagrangian Floer homology
- Analysis of J-holomorphic maps (as time permits).

## Lecture notes

- Chapter 1: Symplectic manifolds (v. 2.0, 18/02/2014)
- Chapter 2: Morse theory (v. 1.0, 06/03/2014)
- Chapter 3: Overview of Lagrangian Floer homology --- first part (v. 2.0, 31/03/2014)
- Chapter 3: Overview of Lagrangian Floer homology --- second part (v. 1.0, 09/04/2014)

(A change in the first version number means a revision of the content. A change in the second version number means a correction of grammar and spelling mistakes.)
## Further bibliography

- D. McDuff and D. Salamon.
* Introduction to symplectic topology, 2nd edition. *
Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York,
1998.
- A. Cannas da Silva.
* Lectures on symplectic geometry. * Lecture Notes in
Mathematics 1764, Springer-Verlag, 2008.
- B. Aebischer, M. Borer, M. Kälin, C. Leuenberger, H. M. Reimann.
* Symplectic geometry.
An introduction based on the seminar in Bern, 1992. * Progress in Mathematics, 124.
Birkhäuser Verlag, Basel, 1994.
- M. Audin and M. Damian.
* Théorie de Morse et homologie de Floer. * Savoirs
Actuels (Les Ulis). EDP Sciences, Les Ulis; CNRS Éditions, Paris, 2010.
- J. Milnor,
* Morse theory. * Annals of Mathematics Studies, No. 51 Princeton University Press, 1963
- D. Salamon,
* Lectures on Floer homology. * In * Symplectic geometry and topology, * Eliashberg and Traynor editors. IAS/Park City Mathematics Series, Volume 7, 1999.