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Knots with Free Period

Published online by Cambridge University Press:  20 November 2018

Richard Hartley
Richard Hartley*
Affiliation:
University of Melbourne, Parkville, Victoria, Australia
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At the Georgia conference in 1961 Fox presented a paper, “Knots and periodic transformations”, in which he asked which knots may be fixed by a periodic transformation of the 3-sphere. He distinguished eight cases according to the type of fixed point set of T and its relationship to the knot. Except for case a), all these cases have since received some attention and conditions have been given for knots to fall into each of these classes. In fact, the problem of deciding which knots fall into category d) (that is “periodic knots“; I will refer to them as cyclically periodic knots) has been the subject of at least six papers [2], [3], [13], [15], [17], [22], but measured by their effectiveness at determining the periods of the knots to nine crossings, the theorems contained in these papers are not entirely satisfactory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 91 - 102
Copyright
Copyright © Canadian Mathematical Society 1981

References

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