Unknotting genus one knots
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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.
17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici Helvetici
17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici Helvetici