Course material

Overview of Lectures

Background on symplectic geometry:

Aebischer, B.; Borer, M.; Kälin, M.; Leuenberger, Ch.; Reimann, H. M.
Symplectic geometry. An introduction based on the seminar in Bern, 1992.
Progress in Mathematics, 124. Birkhduser Verlag, Basel, 1994. xii+239 pp. ISBN: 3-7643-5064-4

Hofer, Helmut; Zehnder, Eduard
Symplectic invariants and Hamiltonian dynamics.
Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks] Birkhäuser Verlag, Basel, 1994. xiv+341 pp. ISBN: 3-7643-5066-0

McDuff, Dusa; Salamon, Dietmar
Introduction to symplectic topology.
Second edition. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998. x+486 pp. ISBN: 0-19-850451-9


Holomorphic curves and Floer homology:

Holomorphic curves in symplectic geometry.
Edited by Michele Audin and Jacques Lafontaine.
Progress in Mathematics, 117. Birkhäuser Verlag, Basel, 1994. xii+328 pp. ISBN: 3-7643-2997-1

McDuff, Dusa; Salamon,Dietmar
J-holomorphic curves and symplectic topology.
American Mathematical Society Colloquium Publications, 52. American Mathematical Society, Providence, RI, 2004. xii+669 pp. ISBN: 0-8218-3485-1

Salamon, Dietmar
Lectures on Floer homology.
Symplectic geometry and topology (Park City, UT, 1997), 143--229, IAS/Park City Math. Ser., 7, Amer. Math. Soc., Providence, RI, 1999


Deligne-Mumford spaces:

H.Hofer, K.Wysocki and E.Zehnder
Deligne-Mumford Theory


J.Robbin and D.Salamon
A construction of the Deligne--Mumford orbifold.
math.SG/0407090


Symplectic field theory:

Y.Eliashberg, A.Givental and H. Hofer
Introduction to symplectic field theory.
GAFA 2000 (Tel Aviv, 1999). Geom. Funct. Anal. 2000, Special Volume, Part II, 560--673.

F.Bourgeois, Y.Eliashberg, H.Hofer, K.Wysocki and E.Zehnder
Compactness results in symplectic field theory.
Geom. Topol. 7 (2003), 799--888

H.Hofer, K.Wysocki and E.Zehnder
Properties of pseudo-holomorphic curves in symplectisations I: Asymptotics.
    Ann. Inst. Henri Poincare, Analyse Nonlineaire, Vol. 13, No.3, 337-379, 1996.
Properties of pseudoholomorphic curves in symplectisations II: Embedding controls and algebraic invariants.
    Geometric and Functional Analysis, Vol. 5 No.2 , 270--328.
Properties of pseudoholomorphic curves in symplectizations III: Fredholm theory.
    in Topics in nonlinear analysis, 381--475, Progr. Nonlinear Differential Equations Appl., 35, Birkhäuser, Basel,1999.
Properties of pseudoholomorphic curves in symplectisation IV: Asymptotics with degeneracies.
    in Contact and symplectic geometry (Cambridge, 1994)}, 78--117, Publ. Newton Inst., 8, Cambridge Univ. Press, Cambridge, 1996.