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On prime noninvertible links

Published online by Cambridge University Press:  17 April 2009

Wilbur Whitten
Affiliation:
University of Southwestern Louisiana, Lafayette, Louisiana, USA.
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Abstract

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It is the purpose of this paper to exhibit an infinite collection of prime, noninvertible links; each link in the collection is the union of two invertible knots. In fact, we present two such families of links. Our examples heuristically indicate that collections of links of this type exist in many varieties.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Fox, R.H., “A quick trip through knot theory”, Topology of 3-manifolds and related topics (Proc. Univ. Georgia Institute, 1961), 120167. (Prentice-Hall, Englewood Cliffs, New Jersey, 1962.)Google Scholar
[2]Hashizume, Yoko, “On the uniqueness of the decomposition of a link”, Osaka J. Math. 10 (1958), 283300.Google Scholar
[3]McPherson, James M., “A family of non-invertible prime links”, Bull. Austral. Math. Soc. 4 (1971), 105108.CrossRefGoogle Scholar
[4]Whitten, W.C. Jr, “A pair of non-invertible links”, Duke Math. J. 36 (1969), 695698.CrossRefGoogle Scholar
[5]Whitten, W.C. Jr, “On noninvertible links with invertible proper sublinks”, Proc. Amer. Math. Soc. 26 (1970), 341346.CrossRefGoogle Scholar