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Braid
computations for the crossing number of Klein links
Michael Bush, Danielle Shepherd, Joseph Smith, Sarah Smith-Polderman, Jennifer Bowen and John Ramsay
Vol. 8 (2015), No. 1, 169–179
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Abstract |
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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 Klein links, where . In combination with previous results, these formulas can be used to calculate the crossing number for any Klein link with given values of and . |
Keywords
knots and links in S3, invariants of knots and 3-manifolds
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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Milestones
Received: 29 January 2014
Revised: 29 May 2014
Accepted: 31 May 2014
Published: 10 December 2014
Communicated by Colin Adams
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Authors |
| Michael Bush | |
| The College of Wooster Wooster, OH 44691 United States |
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| Danielle Shepherd | |
| The College of Wooster Wooster, OH 44691 United States |
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| Joseph Smith | |
| The College of Wooster Wooster, OH 44691 United States |
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| Sarah Smith-Polderman | |
| The College of Wooster Wooster, OH 44691 United States |
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| Jennifer Bowen | |
| The College of Wooster Wooster, OH 44691 United States |
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| John Ramsay | |
| The College of Wooster Wooster, OH 44691 United States |
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