Sakuma, Makoto 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 Cited in 3 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57S17 Finite transformation groups Keywords:isometries of the knot complement; amphicheiral hyperbolic knot; free periods Citations:Zbl 0627.00014 PDFBibTeX XML