The L-move and Markov theorems for trivalent braids

Carmen Caprau; Gabriel Coloma; Marguerite Davis

doi:10.2140/involve.2020.13.21

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arXiv · 1807.08095

The L-move and Markov theorems for trivalent braids

Carmen Caprau·Gabriel Coloma·Marguerite Davis

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Abstract

The L-move for classical braids extends naturally to trivalent braids. We follow the L-move approach to the Markov Theorem, to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this L-Move Markov theorem and prove a more algebraic Markov-type theorem for trivalent braids. Along the way, we provide a proof of the Alexander's theorem analogue for spatial trivalent graphs and trivalent braids.

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Carmen Caprau, Gabriel Coloma, Marguerite Davis. 2018-07-21. The L-move and Markov theorems for trivalent braids. https://doi.org/10.2140/involve.2020.13.21

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