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

Abstract

We give an obstruction for genus one knots $K$, $K^{\prime }$ 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.

5 pages, no Figure

Cited by in corpus (1)

• On the Cosmetic Crossing Conjecture for Special Alternating Links