Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 1 (2015), 169-179.

Braid computations for the crossing number of Klein links

Michael Bush, Danielle Shepherd, Joseph Smith, Sarah Smith-Polderman, Jennifer Bowen, and John Ramsay

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Abstract

Klein links are a nonorientable counterpart to torus knots and links. It is shown that braids representing a subset of Klein links take on the form of a very positive braid after manipulation. Once the braid has reached this form, its number of crossings is the crossing number of the link it represents. Two formulas are proven to calculate the crossing number of K(m,n) Klein links, where m n 1. In combination with previous results, these formulas can be used to calculate the crossing number for any Klein link with given values of m and n.

Article information

Source
Involve, Volume 8, Number 1 (2015), 169-179.

Dates
Received: 29 January 2014
Revised: 29 May 2014
Accepted: 31 May 2014
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370847

Digital Object Identifier
doi:10.2140/involve.2015.8.169

Mathematical Reviews number (MathSciNet)
MR3321718

Zentralblatt MATH identifier
1314.57004

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
knots and links in S3 invariants of knots and 3-manifolds

Citation

Bush, Michael; Shepherd, Danielle; Smith, Joseph; Smith-Polderman, Sarah; Bowen, Jennifer; Ramsay, John. Braid computations for the crossing number of Klein links. Involve 8 (2015), no. 1, 169--179. doi:10.2140/involve.2015.8.169. https://projecteuclid.org/euclid.involve/1511370847


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References

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