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Knots with Free Period
- Source :
- Canadian Journal of Mathematics. 33:91-102
- Publication Year :
- 1981
- Publisher :
- Canadian Mathematical Society, 1981.
-
Abstract
- 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.
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........2386c0b3bf06525135f5c33795a863e7