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An irreducible 4-string braid with unknotted closure

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
University of Liverpool
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Extract

Every oriented knot or link in S3 can be represented in many ways as the closure of a braid β ∈ Bn, the braid group on n strings, for some n. Braids β ∈ Bn, γ ∈ Bm are called closure-equivalent if and are equivalent as oriented knots. It is a well-known result of Markov, see, for example, (l), that β and γ are closure equivalent if and only if there is a sequence of elementary (Markov) moves in which β ∈ Bn is replaced by

(a) a conjugate in Bn, or , or

(c) β1 ∈ Bn−1, where ,

and the process repeated until γ is reached.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 259 - 261
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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