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On a theorem on partially summing tangles by Lickorish

Published online by Cambridge University Press:  24 October 2008

Quách Thi Câm Vân
Affiliation:
University of Geneva

Extract

Kirby and Lickorish have introduced the idea of prime tangle (5) where the term ‘tangle’ is borrowed from Conway (3). While exploring this notion, Lickorish has shown in ((6), theorem 3): A tangle, which is the Conway sum of two tangles, one of which is prime and connected to both arcs of the other one which itself is prime or untangle, is prime.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Bleiler, S. A. Tangles, string primality, and concordance, Ph.D. dissertation (University of Oregon, 1981).Google Scholar
(2)Bonahon, F. and Siebenmann, L. Noeuds algébriques (to appear).Google Scholar
(3)Conway, J. H.An enumeration of knots and links, computational problems in abstract algebra (Pergamon Press, Oxford and New York, 1969), pp. 329358.Google Scholar
(4)Hatcher, A. and Thurston, W. Incompressible surfaces in 2-bridge knot complements (to appear).Google Scholar
(5)Kirby, R. C. and Lickorish, W. B. R.Prime knots and concordance. Math. Proc. Cambridge Philos. Soc. 86 (1979), 437441.CrossRefGoogle Scholar
(6)Lickorish, W. B. R.Prime knots and tangles. Trans. Amer. Math. Soc. 267 (1981), 321332.CrossRefGoogle Scholar
(7)Scharlemann, M. Tunnel number one knots are doubly prime (to appear).Google Scholar