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Floer Homology: Spaces of Trajectories

  • Michèle Audin
  • Mihai Damian
Part of the Universitext book series (UTX)

Abstract

In this chapter we construct the Floer complex for a generic Hamiltonian on a symplectic manifold satisfying a condition on the second homotopy group. The complex is generated by the periodic orbits of fixed Maslov index (a nondegeneracy assumption ensures that they are isolated). We define the differential of the complex using the flow of the gradient of the action functional and we prove that this is indeed a complex. This involves a delicate gluing argument.

Keywords

Vector Field Compact Subset Implicit Function Theorem Symplectic Manifold Maslov Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Michèle Audin
    • 1
  • Mihai Damian
    • 1
  1. 1.IRMAUniversité Louis PasteurStrasbourg CedexFrance

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