Abstract
Let C-T be the subgroup of the smooth knot concordance group generated by topologically slice knots and let C-Delta be the subgroup generated by knots with trivial Alexander polynomial. We prove that C-T/C-Delta 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. (C) 2012 Elsevier Inc. All rights reserved.