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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
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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