CREATING KLEIN BOTTLES BY SURGERY ON KNOTS

Abstract

In the present paper, we will study the creation of Klein bottles by Dehn surgery on knots in the 3-sphere, and we will give an upper bound for slopes creating Klein bottles for non-cabled knots by using the genera of knots. In particular, it is shown that if a Klein bottle is created by Dehn surgery on a genus one knot then the knot is a doubled knot. As a corollary, we obtain that genus one, cross-cap number two knots are doubled knot.