Vol. 13, No. 1, 2020

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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
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 theorem analogue for spatial trivalent graphs and trivalent braids.

Keywords
$L$-moves, Markov-type moves, spatial trivalent graphs, trivalent braids
Mathematical Subject Classification 2010
Primary: 57M15, 57M25
Secondary: 20F36