The L-move and Markov theorems for trivalent braids

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.

27 pages, lots of figures

References in corpus (2)

• Virtual singular braids and links
• Alexander- and Markov-type theorems for virtual trivalent braids

Cited by in corpus (1)

• Diagrammatic representations of knots and links as closed braids