Twisting of Knots along Knotted Solid Tori

Abstract

We twist a knot by twisting some solid tori, each of which contains the knot, one by one to the meridional direction. Suppose the solid tori have mutually disjoint essential toral boundaries in the knot exterior.

M. Kouno, K. Motegi and T. Shibuya have shown that, by twisting a knot along one or two solid tori in an inclusion relation, the resulting knot type is different from the original one (see [5] and [6]). In this paper, we investigate whether twisting along various solid tori also produces a different knot type or not.