An obstruction of Gordian distance one and cosmetic crossings for genus one knots

Tetsuya Ito

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arXiv · 2108.04493

An obstruction of Gordian distance one and cosmetic crossings for genus one knots

Tetsuya Ito

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Abstract

We give an obstruction for genus one knots $K$, $K'$ to have the Gordian distance one by using the $0$th coefficient of the HOMFLT polynomials. As an application, we give a new constraint for genus one knot to admit a (generalized) cosmetic crossing. Combining known results, we prove the (generalized) cosmetic crossing conjecture for genus one pretzel knots.

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Tetsuya Ito. 2021-08-10. An obstruction of Gordian distance one and cosmetic crossings for genus one knots. https://arxiv.org/abs/2108.04493

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