Commentarii Mathematici Helvetici

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Volume 86, Issue 2, 2011, pp. 383–399
DOI: 10.4171/CMH/227

Published online: 2011-02-27

Unknotting genus one knots

Alexander Coward[1] and Marc Lackenby[2]

(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