Unknotting information from Heegaard Floer homology

• Autores: Brendan Owens
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 217, Nº 5, 2008, págs. 2353-2376
• Idioma: inglés
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• Resumen

  • We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of Ozsváth and Szabó's obstruction to unknotting number one. We determine the unknotting numbers of 910, 913, 935, 938, 1053, 10101 and 10120; this completes the table of unknotting numbers for prime knots with crossing number nine or less. Our obstruction uses a refined version of Montesinos' theorem which gives a Dehn surgery description of the branched double cover of a knot