Commentarii Mathematici Helvetici
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Published online: 2011-02-27
Unknotting genus one knotsAlexander Coward and Marc Lackenby (1) University of California at Davis, USA
(2) Oxford University, UK
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.
Keywords: Knot, crossing change, unknotting, genus
Coward Alexander, Lackenby Marc: Unknotting genus one knots. Comment. Math. Helv. 86 (2011), 383-399. doi: 10.4171/CMH/227