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Non-free-periodicity of amphicheiral hyperbolic knots. (English) Zbl 0637.57007

Homotopy theory and related topics, Pap. Symp. Kyoto/Jap. 1984, Adv. Stud. Pure Math. 9, 189-194 (1987).
[For the entire collection see Zbl 0627.00014.]
It is proved that an amphicheiral hyperbolic knot has no free periods. The assertion is obviously not valid for composite knots; the author claims that an amphicheiral prime knot can have only a free period of order two - though no example is known. The proof of the theorem makes use of explicit calculations in PSL(2,\({\mathbb{C}})\) describing the isometries of the hyperbolic knot complement.
Reviewer: G.Burde

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57S17 Finite transformation groups

Citations:

Zbl 0627.00014