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The $L$-move
and Markov theorems for trivalent braids
Carmen Caprau, Gabriel Coloma and Marguerite Davis
Vol. 13 (2020), No. 1, 21–50
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Abstract |
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The -move for classical braids extends naturally to trivalent braids. We follow the -move approach to the Markov theorem to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this -move Markov theorem and prove a more algebraic Markov-type theorem for trivalent braids. Along the way, we provide a proof of the Alexander theorem analogue for spatial trivalent graphs and trivalent braids. |
Keywords
$L$-moves, Markov-type moves, spatial trivalent graphs,
trivalent braids
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Mathematical Subject Classification 2010
Primary: 57M15, 57M25
Secondary: 20F36
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Milestones
Received: 20 July 2018
Accepted: 28 December 2019
Published: 4 February 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Carmen Caprau | |
| Department of Mathematics California State University Fresno, CA 93740-8001 United States |
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| Gabriel Coloma | |
| Department of Mathematical
Sciences University of Puerto Rico Mayagüez Puerto Rico |
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| Marguerite Davis | |
| Department of Mathematics Ithaca College Ithaca, NY United States |
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