Heegaard splittings and Morse-Smale flows - Ralf Gautschi; Joel W. Robbin; Dietmar A. Salamon (International Journal of Mathematics and Mathematical Sciences, 2003)
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.