## Involve: A Journal of Mathematics

• Involve
• Volume 11, Number 4 (2018), 609-624.

#### Abstract

We classify Klein links. In particular, we calculate the number and types of components in a $Kp,q$ Klein link. We completely determine which Klein links are equivalent to a torus link, and which are not.

#### Article information

Source
Involve, Volume 11, Number 4 (2018), 609-624.

Dates
Revised: 9 August 2017
Accepted: 16 August 2017
First available in Project Euclid: 28 March 2018

https://projecteuclid.org/euclid.involve/1522202418

Digital Object Identifier
doi:10.2140/involve.2018.11.609

Mathematical Reviews number (MathSciNet)
MR3778915

Zentralblatt MATH identifier
06864399

#### Citation

Beres, Steven; Coufal, Vesta; Hlavacek, Kaia; Kearney, M. Kate; Lattanzi, Ryan; Olson, Hayley; Pereira, Joel; Strub, Bryan. A classification of Klein links as torus links. Involve 11 (2018), no. 4, 609--624. doi:10.2140/involve.2018.11.609. https://projecteuclid.org/euclid.involve/1522202418

#### References

• C. C. Adams, The knot book, W. H. Freeman and Co., New York, 1994.
• E. Alvarado, S. Beres, V. Coufal, K. Hlavacek, J. Pereira, and B. Reeves, “Klein links and related torus links”, Involve 9:2 (2016), 347–359.
• M. A. Bush, K. R. French, and J. R. H. Smith, “Total linking numbers of torus links and Klein links”, Rose-Hulman Undergrad. Math J. 15:1 (2014), 73–92.
• L. Catalano, D. Freund, R. Ruzvidzo, J. Bowen, and J. Ramsay, “A preliminary study of Klein knots”, pp. 10–17 in Proceedings of the Midstates Conference for Undergraduate Research in Computer Science and Mathematics at Wittenberg University, 2010.
• E. Flapan, Knots, molecules, and the universe: an introduction to topology, American Mathematical Society, Providence, RI, 2016.
• D. Freund and S. Smith-Polderman, “Klein links and braids”, Rose-Hulman Undergrad. Math J. 14:1 (2013), 71–84.
• C. Livingston, Knot theory, Carus Mathematical Monographs 24, Mathematical Association of America, Washington, DC, 1993.
• K. Murasugi, Knot theory and its applications, Birkhäuser, Boston, 1996.
• D. Shepherd, J. Smith, S. Smith-Polderman, J. Bowen, and J. Ramsay, “The classification of a subset of Klein links”, pp. 38–47 in Proceedings of the Midstates Conference for Undergraduate Research in Computer Science and Mathematics at Ohio Wesleyan University, 2012.