Involve: A Journal of Mathematics

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

Klein links and related torus links

Enrique Alvarado, Steven Beres, Vesta Coufal, Kaia Hlavacek, Joel Pereira, and Brandon Reeves

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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,p1, Kp,2 Tp1,2, 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

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

Received: 3 January 2015
Revised: 23 February 2015
Accepted: 26 February 2015
First available in Project Euclid: 22 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

knot theory Klein links torus links


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.

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