Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-29T12:41:37.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Partially Closed Braids

Published online by Cambridge University Press:  20 November 2018

R. S. D. Thomas
R. S. D. Thomas*
Affiliation:
Department Of Computer Science, The University Of Manitoba, WinnipegR3T 2N2
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to define partially closed braids (§3) and to prove that every partially closed braid has a canonical form easily obtainable (§5). These objects are of interest because they can be used to represent knots tied in a string.

Braids have an obvious intuitive meaning to which we shall refer. Braids are also elements of the braid groups of E. Artin [1], defined for each integer n greater than one by the presentation

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 99 - 107
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Artin, E., Theorie der Zöpfe, Abh. Math. Sem. Hamburg 4 (1926), 47-72.Google Scholar
2. Artin, E., The theory of braids, American Scientist 38 (1950), 112-119.Google Scholar
3. D, R. S.. Thomas, 'An Algorithm For Combing Braids', Proc. Second Louisiana Conference On Combinatorics,Graph Theory, And Computing, Baton Rouge, La., 1971, Pp. 517-532.Google Scholar
4. Alexander, J. W., A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 93-95.Google Scholar
5. Reidemeister, K., Knotentheorie (Ergebnisse der Mathematik 1), Berlin, 1932.Google Scholar