International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 247407 | https://doi.org/10.1155/S0161171203210115

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

Received16 Oct 2002

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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