Quasi-alternating Montesinos links

TL;DR

This paper identifies new classes of quasi-alternating Montesinos links, expanding understanding of their properties and providing examples beyond the well-studied alternating links, with implications for knot invariants like Floer and Khovanov homology.

Contribution

The paper introduces previously unknown classes of non-alternating Montesinos links that are quasi-alternating, broadening the scope of these links in knot theory.

Findings

Existence of non-alternating Montesinos links that are quasi-alternating

Quasi-alternating links have computable knot Floer and Khovanov homology

Characterization of new classes of quasi-alternating links

Abstract

The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot Floer homology detects the genus of a knot as well as whether a knot is fibered, as provided bounds on unknotting number and slice genus, characterization of quasi-alternating links becomes an interesting open problem. We show that there exist classes of non-alternating Montesinos links, which are quasi-alternating.