Quasipositivity and braid index of pretzel knots
arXiv:2205.05347 · doi:10.4310/CAG.241121001754
Abstract
This short note is about three-stranded pretzel knots that have an even number of crossings in one of the strands. We calculate the braid index of such knots and determine which of them are quasipositive. The main tools are the Morton-Franks-Williams inequalities, and Khovanov-Rozansky concordance homomorphisms.
arXiv comment6 pages, 2 figures. v2: Minor changes. Accepted for publication in Communications in Analysis and Geometry. Comments welcome