Characterization of quasi-alternating Montesinos links

Let L be a quasi-alternating link at a crossing c. We construct an infinite family of quasi-alternating links from L by replacing the crossing c by a product of rational tangles, each of which extends c. Consequently, we determine an infinite family of quasi-alternating Montesinos links. This family includes all classes of quasi-alternating Montesinos links that have been detected by Widmer [Quasi-alternating Montesinos links, J. Knot Theory Ramifications 18(10) (2009) 1459-1469]. We conjecture that this family contains all non-alternating quasi-alternating Montesinos links.