THE JONES POLYNOMIAL OF KNOTS WITH SYMMETRIC UNION PRESENTATIONS

Title & Authors
THE JONES POLYNOMIAL OF KNOTS WITH SYMMETRIC UNION PRESENTATIONS
Tanaka, Toshifumi;

Abstract
A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are symmetric with respect to an axis in the 2-plane, by connecting them with 2-tangles with twists along the axis and 2-tangles with no twists. This paper presents an invariant of knots with symmetric union presentations, which is called the minimal twisting number, and the minimal twisting number of $\small{10_{42}}$ is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.
Keywords
symmetric union;Jones polynomial;ribbon knot;
Language
English
Cited by
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