Unknotting information from Heegaard Floer homology

Brendan Owens

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Unknotting information from Heegaard Floer homology

Brendan Owens

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Abstract

We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of Ozsvath and Szabo's obstruction to unknotting number one. We determine the unknotting numbers of 9_10, 9_13, 9_35, 9_38, 10_53, 10_101 and 10_120; 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.

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Brendan Owens. 2005-06-23. Unknotting information from Heegaard Floer homology. https://arxiv.org/abs/math/0506485

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