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arXiv:2108.04493 [math.GT]AbstractReferencesReviewsResources

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

Tetsuya Ito

Published 2021-08-10Version 1

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.

Comments: 5 pages, no Figure
Categories: math.GT
Subjects: 57K10
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