Geometric types of twisted knots
Let be a knot in the -sphere , and a disk in meeting transversely in the interior. For non-triviality we assume that over all isotopies of in . Let () be a knot obtained from by twistings along the disk . If the original knot is unknotted in , we call a . We describe for which pair and an integer , the twisted knot is a torus knot, a satellite knot or a hyperbolic knot.