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Klein links and related torus links. (English) Zbl 1337.57006

Summary: 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 \(p\geq 5\) is odd, is equivalent to a torus link.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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