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.