Owens, B. and Strle, S. (2016) Immersed disks, slicing numbers and concordance unknotting numbers. Communications in Analysis and Geometry, 24(5), pp. 1107-1138. (doi: 10.4310/CAG.2016.v24.n5.a8)
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Abstract
We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes required to obtain a slice knot; and the concordance unknotting number, which is the minimal unknotting number in a smooth concordance class. Using Heegaard Floer homology we obtain bounds that can be used to determine two of these invariants for all prime knots with crossing number ten or less, and to determine the concordance unknotting number for all but thirteen of these knots. As a further application we obtain some new bounds on Gordian distance between torus knots. We also give a strengthened version of Ozsváth and Szabó’s obstruction to unknotting number one.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Owens, Professor Brendan |
| Authors: | Owens, B., and Strle, S. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Communications in Analysis and Geometry |
| Journal Abbr.: | Comm. Anal. Geom. |
| Publisher: | International Press |
| ISSN: | 1019-8385 |
| ISSN (Online): | 1944-9992 |
| Copyright Holders: | Copyright © 2016 International Press |
| First Published: | First published in Communications in Analysis and Geometry 24(5):1107-1138 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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