Detection of knots and a cabling formula for A-polynomials

Abstract

We say that a given knot J ⊂ S^3 is detected by its knot Floer homology and AA–polynomial if whenever a knot K ⊂ S^3 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 S^3 each of which is detected by its knot Floer homology and AA–polynomial. In addition we give a cabling formula for the AA–polynomials of cabled knots in S^3, which is of independent interest. In particular we give explicitly the AA–polynomials of iterated torus knots.