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Closed braids which are not prime knots

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
Affiliation:
University of Liverpool

Extract

An element BBn, the braid group on n strings, which can be written as

in terms of the standard generators of Bn is called a split braid. It is easy to see that the resulting closed braid is the connected sum of the closed braids Ĉ and on k + 1 and nk strings respectively (figure 1).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Artin, E.Theorie der Zöpfe. Hamburg Abh. 4 (1925), 4772.CrossRefGoogle Scholar
(2)Birman, J. S.Braids, links and mapping-class groups. Annals of Maths. Studies 82 (1974).Google Scholar
(3)Morton, H. R.Infinitely many fibred knots having the same Alexander polynomial. Topology 17 (1978), 101–4.CrossRefGoogle Scholar
(4)Murasugi, K.On closed 3.braids. Mem. Amer. Math. Soc. 151.Google Scholar