Composite Knots Obtained by Twisting Torus Knots

초록

A twisted torus knot is obtained from a torus knot by performing full twists on some adjacent strands of the torus knot. Morimoto constructed infinitely many twisted torus knots which are composite knots and he conjectured that his knots are all of composite twisted torus knots. We show that his conjecture is almost true by giving a complete list of such twisted torus knots.