Klein links and related torus links

Abstract

In this paper, we present our constructions and results leading up to our discovery of a class of Klein links that are not equivalent to any torus links. In particular, we calculate the number and types of components in a $K_{p,q}$ Klein link and show that $K_{p,p}\equiv K_{p,p-1}$, $K_{p,2}\equiv T_{p-1,2}$, and $K_{2p,2p}\equiv T_{2p,p}$. Finally, we show that in contrast to the fact that every Klein knot is a torus knot, no Klein link $K_{p,p}$, where $p\ge 5$ is odd, is equivalent to a torus link.