MAT 645 Introduction to Floer theory Joa Weber, Spring 2000 TU TH 9.50-11.10am, MATH 5-127

Main text we follow

• [Sa1] Salamon D.A., Lectures on Floer homology (1430kB), Lecture Notes for the IAS/PCMI Graduate Summer School on Symplectic Geometry and Topology, Preprint, December 1997. In  Synplectic Geometry and Topology,  edited by Y. Eliashberg and L. Traynor, IAS/Park City Mathematics series, Vol 7, 1999, pp. 143--230.

Morse theory

• Background in differential topology and dynamical systems
• [Hi] Hirsch M.W., Differential topology, Corrected reprint of the 1976 original. Graduate Texts in Mathematics, 33, Springer-Verlag, New York, 1994.
• [PdM] Palis J.Jr., de Melo W., Geometric theory of dynamical systems. An introduction. Translated from the Portuguese by A. K. Manning. Springer-Verlag, New York-Berlin, 1982.
• Foundations
• [Mi] Milnor J., Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963 vi+153 pp.
• Morse homology
• [Sch]Schwarz M., Morse homology. Progress in Mathematics, 111. Birkhäuser Verlag, Basel, 1993.
• [Wi] Witten E., Supersymmetry and Morse theory. J. Differential Geom. 17 (1982), no. 4, 661--692 (1983).

Symplectic geometry

• [McDS1] McDuff D., Salamon D.A., Introduction to Symplectic Topology, Oxford University Press, April 1995.

- foundational material of symplectic geometry in part I

• Some analytical background
• [McDS2]    McDuff D., Salamon D.A., J-holomorphic Curves and Quantum Cohomology, AMS, University Lecture Series, Vol. 6, Providence, Rhode Island, 1994.

Some history of the weak non-degenerate Arnold conjecture

• monotone case
• [Fl1] Floer, A., Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575--611.
• weakly monotone case
• [HS1] Hofer H., Salamon D.A., Floer homology and Novikov rings, The Floer Memorial Volume, edited by H. Hofer, C. Taubes, A. Weinstein, and E. Zehnder, Birkhäuser 1995, pp 483-524. paper
• [On1] Ono K., On the Arnol'd conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995), no. 3, 519--537.
• general case
• [FO] Fukaya K., Ono K., Arnold conjecture and Gromov-Witten invariant, Topology 38 (1999), no. 5, 933--1048.
• [LT] Liu G., Tian G., Floer homology and Arnold conjecture, J. Differential Geom, 49 (1998), no. 1, 1--74. paper
• [Ru] Ruan Y., Virtual neighborhoods and pseudo-holomorphic curves, Proceedings of 6th Gökova Geometry-Topology Conference. Turkish J. Math. 23 (1999), no. 1, 161--231. preprint

 

Remark: Some links refer to .dvi, .pdf or .ps files. Configuration of netscape to start automatically an appropriate viewer such as xdvi, ghostview or the Adobe acrobat pdf-reader is recommended. Let me know in case you have trouble with that.