Detection of knots and a cabling formula for A–polynomials

We say that a given knot J ⊂ S³ is detected by its knot Floer homology and A–polynomial if whenever a knot K ⊂ S³ has the same knot Floer homology and the same A–polynomial as J, then K = J. In this paper we show that every torus knot T(p, q) is detected by its knot Floer homology and A–polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S³ each of which is detected by its knot Floer homology and A–polynomial. In addition we give a cabling formula for the A–polynomials of cabled knots in S^3, which is of independent interest. In particular we give explicitly the A–polynomials of iterated torus knots.