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)

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, Professor 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