A Simple Characterization of Adequate Links

Abstract

We prove that the Jones diameter of a link is twice its crossing number whenever the breadth of its Jones polynomial equals the difference between the crossing number and the Turaev genus. This implies that such link is adequate, as per the characterization provided in [5, Theorem 1.1]. By combining this with the result in [1, Theorem 3.2], we obtain a characterization of adequate links using these numerical link invariants. As an application, we provide a criterion to obstruct a link from being quasi-alternating. Furthermore, we establish a lower bound for the crossing number of certain classes of links, aiding in determining the crossing number of the link in specific cases.