Unknotting information from Heegaard Floer homology

Owens, B. (2008) Unknotting information from Heegaard Floer homology. Advances in Mathematics, 217(5), pp. 2353-2376. (doi:10.1016/j.aim.2007.10.006)

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Abstract

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.

Item Type:Articles
Keywords:Unknotting number, Heegaard Floer homology
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Owens, Dr Brendan
Authors: Owens, B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Journal Abbr.:Adv. Math.
Publisher:Elsevier
ISSN:0001-8708
ISSN (Online):1090-2082
Published Online:07 February 2008
Copyright Holders:Copyright © 2008 Elsevier
First Published:First published in Advances in Mathematics 217(5):2353-2376
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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