Topologically slice knots with nontrivial Alexander polynomial

Let CT be the subgroup of the smooth knot concordance group generated by topologically slice knots and let CΔ be the subgroup generated by knots with trivial Alexander polynomial. We prove that CT/CΔ is infinitely generated. Our methods reveal a similar structure in the 3-dimensional rational spin bordism group, and lead to the construction of links that are topologically, but not smoothly, concordant to boundary links.