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Organizers |
on simple ribbon knots
by
Tatsuya Tsukamoto
Osaka Institute of Technology
Coauthors: Kengo Kishimoto, Tetsuo Shibuya
An m-ribbon fusion on a link L is an m-fusion of L and an m-component trivial link O which is split from L and each of whose components is attatched by a unique band to a component of L. Note that any ribbon knot can be obtained from the trivial knot by a ribbon fusion.
The m-ribbon fusion is called a simple ribbon fusion if O bounds m mutually disjoint disks D which are split from L such that each disk of D intersects with one of the bands B for the ribbon fusion exactly once at a single arc of ribbon type and each band of B intersects with one disk of D exactly once.
We call a knot obtained from the trivial knot by a finite sequence of simple ribbon fusions a simple ribbon knot. All ribbon knots with no more than 9 crossings, Kinoshita-Terasaka knot, and Kanenobu knots are simple ribbon knots. In this talk we give a necessary condition for satellite knots to be simple ribbon knots. As a consequence, we show that a (p,q)-cable of any ribbon knot (p>1) is not a simple ribbon knot.
Date received: December 12, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-52.