# Strongly quasipositive quasi-alternating links and Montesinos links

## TL;DR

This paper characterizes strongly quasipositive quasi-alternating links and identifies new classes of such links among Montesinos links, establishing conditions under which these links are definite and strongly quasipositive.

## Contribution

It provides a characterization of strongly quasipositive quasi-alternating links and detects new classes of strongly quasipositive Montesinos links based on their properties.

## Key findings

- Strongly quasipositive quasi-alternating links are characterized by definiteness.
- New classes of strongly quasipositive Montesinos links are identified.
- Conditions involving quasi-alternating crossings and properties of the link components are established.

## Abstract

The aim of this article is to give a characterization of strongly quasipositive quasi-alternating links and detect new classes of strongly quasipositive Montesinos links and non-strongly quasipositive Montesinos links. In this direction, we show that, if $L$ is an oriented quasi-alternating link with a quasi-alternating crossing $c$ such that $L_0$ is alternating (where $L_0$ has the induced orientation), then $L$ is definite if and only if it is strongly quasipositive (up to mirroring). We also show that if $L$ is an oriented quasi-alternating link with a quasi-alternating crossing $c$ such that $L_0$ is fibred or more generally has a unique minimal genus Seifert surface (where $L_0$ has the induced orientation), then $L$ is definite if and only if it is strongly quasipositive (up to mirroring).