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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Hindawi Limited
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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doaj-33e7cee6d7ca4f09a48f4bd952d7347b2020-11-24T21:57:24ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003563539357210.1155/S0161171203210115Heegaard splittings and Morse-Smale flowsRalf Gautschi0Joel W. Robbin1Dietmar A. Salamon2Navigation Support Office, European Space Operations Center, Robert-Bosch Straße 5, Darmstadt D-64293, GermanyMathematics Department, University of Wisconsin, Madison, WI 53706, USADepartment of Mathematics, ETH Zürich, Zürich 8092, SwitzerlandWe 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.http://dx.doi.org/10.1155/S0161171203210115 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ralf Gautschi Joel W. Robbin Dietmar A. Salamon |
| spellingShingle |
Ralf Gautschi Joel W. Robbin Dietmar A. Salamon Heegaard splittings and Morse-Smale flows International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Ralf Gautschi Joel W. Robbin Dietmar A. Salamon |
| author_sort |
Ralf Gautschi |
| title |
Heegaard splittings and Morse-Smale flows |
| title_short |
Heegaard splittings and Morse-Smale flows |
| title_full |
Heegaard splittings and Morse-Smale flows |
| title_fullStr |
Heegaard splittings and Morse-Smale flows |
| title_full_unstemmed |
Heegaard splittings and Morse-Smale flows |
| title_sort |
heegaard splittings and morse-smale flows |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171203210115 |
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AT ralfgautschi heegaardsplittingsandmorsesmaleflows AT joelwrobbin heegaardsplittingsandmorsesmaleflows AT dietmarasalamon heegaardsplittingsandmorsesmaleflows |
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1725855709706321920 |