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)
Text
25283.pdf 358kB |
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 |
University Staff: Request a correction | Enlighten Editors: Update this record