Symplectic fixed points and holomorphic spheres

@article{Floer1989SymplecticFP,
  title={Symplectic fixed points and holomorphic spheres},
  author={Andreas Floer},
  journal={Communications in Mathematical Physics},
  year={1989},
  volume={120},
  pages={575-611}
}
  • A. Floer
  • Published 1989
  • Mathematics
  • Communications in Mathematical Physics
LetP be a symplectic manifold whose symplectic form, integrated over the spheres inP, is proportional to its first Chern class. On the loop space ofP, we consider the variational theory of the symplectic action function perturbed by a Hamiltonian term. In particular, we associate to each isolated invariant set of its gradient flow an Abelian group with a cyclic grading. It is shown to have properties similar to the homology of the Conley index in locally compact spaces. As an application, we… Expand
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The notion of a Morse index of a function on a finite-dimensional manifold cannot be generalized directly to the symplectic action function a on the loop space of a manifold. In this paper, we defineExpand
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