We say that a given knot is detected by its knot Floer homology and –polynomial if whenever a knot has the same knot Floer homology and the same –polynomial as , then . In this paper we show that every torus knot is detected by its knot Floer homology and –polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in each of which is detected by its knot Floer homology and –polynomial. In addition we give a cabling formula for the –polynomials of cabled knots in , which is of independent interest. In particular we give explicitly the –polynomials of iterated torus knots.
"Detection of knots and a cabling formula for $A$–polynomials." Algebr. Geom. Topol. 17 (1) 65 - 109, 2017. https://doi.org/10.2140/agt.2017.17.65