THE JONES POLYNOMIAL OF KNOTS WITH SYMMETRIC UNION PRESENTATIONS Tanaka, Toshifumi;
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 is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.
symmetric union;Jones polynomial;ribbon knot;
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