## Involve: A Journal of Mathematics

• Involve
• Volume 9, Number 2 (2016), 347-359.

#### 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 $Kp,q$ Klein link and show that $Kp,p ≡ Kp,p−1$, $Kp,2 ≡ Tp−1,2$, and $K2p,2p ≡ T2p,p$. Finally, we show that in contrast to the fact that every Klein knot is a torus knot, no Klein link $Kp,p$, where $p ≥ 5$ is odd, is equivalent to a torus link.

#### Article information

Source
Involve, Volume 9, Number 2 (2016), 347-359.

Dates
Revised: 23 February 2015
Accepted: 26 February 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371005

Digital Object Identifier
doi:10.2140/involve.2016.9.347

Mathematical Reviews number (MathSciNet)
MR3470736

Zentralblatt MATH identifier
1337.57006

#### Citation

Alvarado, Enrique; Beres, Steven; Coufal, Vesta; Hlavacek, Kaia; Pereira, Joel; Reeves, Brandon. Klein links and related torus links. Involve 9 (2016), no. 2, 347--359. doi:10.2140/involve.2016.9.347. https://projecteuclid.org/euclid.involve/1511371005

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