Woven Braids and their Closures

Details Woven Braids and their Closures Woven Braids and their Closures

1995-12-31

arxiv.org/abs/q-alg/9512033v1

Mathematics

Quantum Algebra

12 pages, latex, 4 figures

Scientific paper

A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots, we get the 'woven version' of the well-known theorem of Markov, giving moves that are capable of producing all woven braids with equivalent closures. As corollary we obtain that a link in which each component is dyed with at least two colours can be projected onto a plane without crossing strands of the same colour. Finally a table of minimal woven braids for all nine crossing knots is appended.

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