Cable knots obtained by positively twisting torus knots

Abstract

The twisted torus knot [Formula: see text] is a knot obtained from the torus knot [Formula: see text] by twisting [Formula: see text] adjacent stands fully [Formula: see text] times. If [Formula: see text] or [Formula: see text] is a multiple of [Formula: see text], then [Formula: see text] is known to be a cable of a nontrivial knot or a torus knot. Assuming that [Formula: see text] and [Formula: see text] is not a multiple of [Formula: see text], we determine the parameters [Formula: see text] for which the positively twisted torus knot [Formula: see text] is a cable knot.