Fibonacci numbers and the “fibered” Bleiler conjecture. (English) Zbl 0970.57003

Stoimenow, A.

Int. Math. Res. Not. 2000, No. 23, 1207-1212 (2000).

The author proves that a fibered 2-bridge knot of unknotting number 1 realizes its unknotting number in the diagram of all Conway coefficients even. For related work see K. Taniyama [Math. Ann. 291, No. 4, 579-590 (1991; Zbl 0726.57009)], T. Kanenobu and H. Murakami [Proc. Am. Math. Soc. 98, 499-502 (1986; Zbl 0613.57002)].

Reviewer: Michael Heusener (Aubière)

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

rational knots; two-bridge knots; unknotting number

Citations:

Zbl 0613.57002; Zbl 0726.57009; Zbl 0739.57005