A New property of quasi-alternating links

TL;DR

This paper establishes a new inequality relating crossing number and determinant for quasi-alternating links, proposing a conjecture that could simplify identifying such links.

Contribution

It introduces a new property linking crossing number and determinant for quasi-alternating links and conjectures this as a general rule.

Findings

Crossing number is less than or equal to the determinant for known quasi-alternating links.

Proposes a conjecture that this inequality holds for all quasi-alternating links.

Potentially simplifies the process of detecting quasi-alternating links.

Abstract

We show that the crossing number of any link that is known to be quasi-alternating is less than or equal to its determinant. Based on this, we conjecture that the crossing number of any quasi-alternating link is less than or equal to its determinant. Thus, if this conjecture is proved then it would give an easier obstruction for quasi-alternateness than the ones already known.