# The classification of quasi-alternating Montesinos links

## TL;DR

This paper completes the classification of quasi-alternating Montesinos links, showing they match previously identified classes and linking their properties to topological invariants like L-spaces and definite 4-manifolds.

## Contribution

It finalizes the classification of quasi-alternating Montesinos links and establishes a topological characterization involving double branched covers and 4-manifold bounds.

## Key findings

- Quasi-alternating Montesinos links are exactly those previously identified.
- A Montesinos link is quasi-alternating if its double branched cover is an L-space.
- Such links bound both positive and negative definite 4-manifolds with trivial first homology.

## Abstract

In this note, we complete the classification of quasi-alternating Montesinos links. We show that the quasi-alternating Montesinos links are precisely those identified independently by Qazaqzeh-Chbili-Qublan and Champanerkar-Ording. A consequence of our proof is that a Montesinos link $L$ is quasi-alternating if and only if its double branched cover is an L-space, and bounds both a positive definite and a negative definite 4-manifold with vanishing first homology.