Signatures of iterated torus knots

Abstract

By an iterated torus knot I mean a knot obtained by starting with a torus knot, taking a cable about it, then a cable about the result, and so on. One reason why this class of knots is interesting is that it contains the class of all one-component links of isolated singularities of complex algebraic plane curves (i.e. all algebraic knots). Recently, Lee Rudolph has asked [Ru] whether A is an independent set in the knot cobordism group. Independence may be interpreted in any sense you desire; in particular Rudolph asks whether