Twisting quasi-alternating links

TL;DR

This paper explores the properties of quasi-alternating links, demonstrating how they can generate infinite families through rational tangle replacements and analyzing their homological thickness, especially in pretzel links.

Contribution

It introduces a method to produce infinite quasi-alternating link families via rational tangles and characterizes the homological properties of pretzel links.

Findings

Many pretzel links are quasi-alternating.

The homological thickness of Khovanov homology for these links is determined.

Infinite families of quasi-alternating links can be generated systematically.

Abstract

Quasi-alternating links are homologically thin for both Khovanov homology and knot Floer homology. We show that every quasi-alternating link gives rise to an infinite family of quasi-alternating links obtained by replacing a crossing with an alternating rational tangle. Consequently, we show that many pretzel links are quasi-alternating, and we determine the thickness of Khovanov homology for "most" pretzel links with arbitrarily many strands.