Unknotting genus one knots

Details Unknotting genus one knots Unknotting genus one knots

2008-09-24

arxiv.org/abs/0809.4142v3

Mathematics

Geometric Topology

17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici Helveti

Scientific paper

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.

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