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On the splitting field of the Alexander polynomial of a periodic knot

Published online by Cambridge University Press:  17 April 2009

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
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Abstract

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We show that the Murasugi conditions for the Alexander polynomial of a cyclically periodic knot imply a modified form of the Burde-Trotter condition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 313 - 315
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Burde, G., ‘Uber periodische Knoten’, Arch. Math. (Basel) 30 (1978), 487–492.CrossRefGoogle Scholar
[2]Burde, G. and Zieschang, H., Knots, Studies in Mathematics 5 (W. de Gruyter, Berlin, New York, 1985).Google Scholar
[3]Davis, J.M. and Livingston, C., ‘Alexander polynomials of periodic knots’, Topology 30 (1991), 551–564.CrossRefGoogle Scholar
[4]Hillman, J.A., Alexander Ideals of Links, Lecture Notes in Mathematics 895 (Springer-Verlag, Berlin, Heidelberg, New York, 1981).CrossRefGoogle Scholar
[5]Hillman, J.A., ‘New proofs of two theorems on periodic knots’, Arch. Math. (Basel) 37 (1981), 457–461.CrossRefGoogle Scholar
[6]Hillman, J.A., ‘On the Alexander polynomial of a cyclically periodic knot’, Proc. Amer. Math. Soc. 89 (1983), 155–156.CrossRefGoogle Scholar
[7]Murasugi, K., ‘On periodic knots’, Comment. Math. Helv. 46 (1971), 162–174.CrossRefGoogle Scholar
[8]Trotter, H.F., ‘Periodic automorphisms of groups and knots’, Duke Math. J. 28 (1961), 553–557.CrossRefGoogle Scholar