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Heegaard splittings and Morse-Smale flows

Author

Listed:
  • Ralf Gautschi
  • Joel W. Robbin
  • Dietmar A. Salamon

Abstract

We describe three theorems which summarize what survives in three dimensions of Smale's proof of the higher-dimensional Poincaré conjecture. The proofs require Smale's cancellation lemma and a lemma asserting the existence of a 2 -gon. Such 2 -gons are the analogues in dimension two of Whitney disks in higher dimensions. They are also embedded lunes; an (immersed) lune is an index-one connecting orbit in the Lagrangian Floer homology determined by two embedded loops in a 2 -manifold.

Suggested Citation

  • Ralf Gautschi & Joel W. Robbin & Dietmar A. Salamon, 2003. "Heegaard splittings and Morse-Smale flows," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-34, January.
    • Handle: RePEc:hin:jijmms:247407
    DOI: 10.1155/S0161171203210115
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