Twisting of knots along knotted solid tori (Q690142)

The paper extends work of Kouno, Motegi and Shibuya on constructing new knots from a given satellite knot by twisting about meridian curves of the essential tori in its exterior. In an analysis of the resulting knot in terms of the Jaco-Shalen-Johannson decomposition of its exterior, the author shows that in a wide range of cases the twisted knot is not equivalent to the original. He also identifies some conditions under which the knot is unaltered by certain twists.