Heegaard splittings and Morse-Smale flows

Ralf Gautschi, Joel W. Robbin and Dietmar A. Salamon

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-34

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:247407

DOI: 10.1155/S0161171203210115

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