Heegaard diagrams and Floer homology

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13 Scopus citations

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 languageEnglish (US)
Pages1083-1099
Number of pages17
StatePublished - Dec 1 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Ozsváth, P., & Szabó, Z. (2006). Heegaard diagrams and Floer homology. 1083-1099. Paper presented at 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain.