Klein links and related torus links

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 ≡ K_p,p−1, K_p,2 ≡ T_p−1,2, and K_2p,2p ≡ 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 ≥ 5 is odd, is equivalent to a torus link.