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On two-bridged knot polynomials

Published online by Cambridge University Press:  09 April 2009

R. I. Hartley
R. I. Hartley
Affiliation:
Department of Mathematics University of MelbourneParkville 3052 Victoria, Australia
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Abstract

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The extended diagram of a two-bridged knot is introduced, and it is shown how the coefficients of the Alexander polynomial of the knot may be read straight from this diagram. Using this result, it is shown by diagram manipulation that a conjecture of Fox about the coefficients of the Alexander polynomial of an alternating knot is true at least for two-bridged knots (which are all alternating).

1980 Mathematics subject classification (Amer. Math. Soc.): 57 M 25.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 241 - 249
Copyright
Copyright © Australian Mathematical Society 1979

References

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