Braid Floer homology

@article{Berg2009BraidFH,
  title={Braid Floer homology},
  author={J. V. D. Berg and R. Ghrist and R. Vandervorst and W. W{\'o}jcik},
  journal={arXiv: Dynamical Systems},
  year={2009}
}
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of the Floer homology originally used for the Arnol'd Conjecture yields a Morse-type forcing theory for periodic points of area-preserving diffeomorphisms of the 2-disc based on… Expand
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