Linear independence of Whitehead Doubles of Torus knots in the smooth Concordance group

We show that the untwisted Whitehead doubles of the (2, 2^k-1) torus knots freely generate a
free abelian subgroup of the kernel of the homomorphism from the smooth knot concordance group
to the topological knot concordance group. The method uses an argument of Furuta using SO(3) instanton moduli spaces
and calculations of Chern-Simons invariants of flat SO(3) connections on 2-fold branched covers. (joint work with Matt Hedden).