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2015 Braid computations for the crossing number of Klein links
Michael Bush, Danielle Shepherd, Joseph Smith, Sarah Smith-Polderman, Jennifer Bowen, John Ramsay
Involve 8(1): 169-179 (2015). DOI: 10.2140/involve.2015.8.169

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.

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Michael Bush. Danielle Shepherd. Joseph Smith. Sarah Smith-Polderman. Jennifer Bowen. John Ramsay. "Braid computations for the crossing number of Klein links." Involve 8 (1) 169 - 179, 2015. https://doi.org/10.2140/involve.2015.8.169

Information

Received: 29 January 2014; Revised: 29 May 2014; Accepted: 31 May 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1314.57004
MathSciNet: MR3321718
Digital Object Identifier: 10.2140/involve.2015.8.169

Subjects:
Primary: 57M25 , 57M27

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

Rights: Copyright © 2015 Mathematical Sciences Publishers

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