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arXiv · 1305.3455

Unknotting number and genus of 3-braid knots

Eon-Kyung Lee·Sang-Jin Lee
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Abstract

Let $u(K)$ and $g(K)$ denote the unknotting number and the genus of a knot $K$, respectively. For a 3-braid knot $K$, we show that $u(K)\le g(K)$ holds, and that if $u(K)=g(K)$ then $K$ is either a 2-braid knot, a connected sum of two 2-braid knots, the figure-eight knot, a strongly quasipositive knot or its mirror image.

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Eon-Kyung Lee, Sang-Jin Lee. 2014-01-27. Unknotting number and genus of 3-braid knots. https://doi.org/10.1142/s0218216513500478

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