Abstract
We review the construction of Heegaard-Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the case of the Conway link.
| Original language | English (US) |
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| Pages | 1083-1099 |
| Number of pages | 17 |
| State | Published - 2006 |
| Event | 25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: Aug 22 2006 → Aug 30 2006 |
Other
| Other | 25th International Congress of Mathematicians, ICM 2006 |
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| Country/Territory | Spain |
| City | Madrid |
| Period | 8/22/06 → 8/30/06 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Floer homology
- Heegaard diagrams
- Thurston norm