Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology

1. Front Matter

   Pages I-XIV

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2. LECTURES ON THE MORSE COMPLEX FOR INFINITE-DIMENSIONAL MANIFOLDS

   • ALBERTO ABBONDANDOLO, PIETRO MAJER

   Pages 1-74

3. NOTES ON FLOER HOMOLOGY AND LOOP SPACE HOMOLOGY

   • ALBERTO ABBONDANDOLO, MATTHIAS SCHWARZ

   Pages 75-108

4. HOMOTOPICAL DYNAMICS IN SYMPLECTIC TOPOLOGY

   • JEAN-FRANÇOIS BARRAUD, OCTAV CORNEA

   Pages 109-148

5. MORSE THEORY, GRAPHS, AND STRING TOPOLOGY

   • RALPH L. COHEN

   Pages 149-184

6. TOPOLOGY OF ROBOT MOTION PLANNING

   • MICHAEL FARBER

   Pages 185-230

7. APPLICATION OF FLOER HOMOLOGY OF LANGRANGIAN SUBMANIFOLDS TO SYMPLECTIC TOPOLOGY

   • KENJI FUKAYA

   Pages 231-276

8. THE LS-INDEX: A SURVEY

   • MAREK IZYDOREK

   Pages 277-320

9. LECTURES ON FLOER THEORY AND SPECTRAL INVARIANTS OF HAMILTONIAN FLOWS

   • YONG-GEUN OH

   Pages 321-416

10. FLOER HOMOLOGY, DYNAMICS AND GROUPS

    • LEONID POLTEROVICH

    Pages 417-438

11. SYMPLECTIC TOPOLOGY AND HAMILTON– JACOBI EQUATIONS

    • CLAUDE VITERBO

    Pages 439-459

12. Back Matter

    Pages 461-462

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The papers collected in this volume are contributions to the 43rd session of the Seminaire ´ de mathematiques ´ superieures ´ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ´ de Montreal ´ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ´ , our administrative assistant, for her help with the organi- tion and Mr. Andre ´ Montpetit, our technical editor, for his help in the preparation of the volume.

• Boundary value problem
• Floer homology
• Homotopy
• Loop group
• cohomology
• differential topology
• homology
• partial differential equations

• Tel-Aviv University, Israel

  Paul Biran

• University of Montreal, Canada

  Octav Cornea, François Lalonde

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