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 2-gon. Such 2-gons are the analogues in dimension two of Whitn...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203210115 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |