Ralf Gautschi, Joel W. Robbin, Dietmar A. Salamon, "Heegaard splittings and Morse-Smale flows", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 247407, 34 pages, 2003. https://doi.org/10.1155/S0161171203210115
Heegaard splittings and Morse-Smale flows
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 -gon. Such -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 -manifold.
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