dorsal/arxiv
View SchemaWoven Braids and their Closures
| Authors | Jan A. Kneissler |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9512033 |
| URL | https://arxiv.org/abs/q-alg/9512033 |
Abstract
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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"abstract": "A special class of braids, called woven, is introduced and it is shown that\nevery conjugation class of the braid group contains woven braids. In\nconsequence, links can be presented as plats or closures of woven braids.\nRestricting on knots, we get the \u0027woven version\u0027 of the well-known theorem of\nMarkov, giving moves that are capable of producing all woven braids with\nequivalent closures. As corollary we obtain that a link in which each component\nis dyed with at least two colours can be projected onto a plane without\ncrossing strands of the same colour. Finally a table of minimal woven braids\nfor all nine crossing knots is appended.",
"arxiv_id": "q-alg/9512033",
"authors": [
"Jan A. Kneissler"
],
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"q-alg",
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"title": "Woven Braids and their Closures",
"url": "https://arxiv.org/abs/q-alg/9512033"
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