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Threading knot diagrams

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
Department of Pure Mathematics, University of LiverpoolL69 3BX
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Extract

Alexander [1] showed that an oriented link K in S3 can always be represented as a closed braid. Later Markov [5] described (without full details) how any two such representations of K are related. In her book [3], Birman gives an extensive description, with a detailed combinatorial proof of both these results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 247 - 260
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Alexander, J. W.. A lemma on systems of knotted curves. Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 93–95.CrossRefGoogle ScholarPubMed
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[3]Birman, J. S.. Braids, Links and Mapping Class Groups. Ann. of Math. Stud. 82 (1974).Google Scholar
[4]Jones, V. F. R.. A polynomial invariant for knots via von Neumann algebras. Bull. Amer. Math. Soc. 12 (1985), 103–111.CrossRefGoogle Scholar
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[7]Rudolph, L.. Special positions for surfaces bounded by closed braids. Preprint 1984, Box 251, Adamsville, Rhode Island.Google Scholar