Abstract
We investigate the concordance properties of "parallel links" P (K), given by the (2, 0) cable of a knot K. We focus on the question: if P (K) is concordant to a split link, is K necessarily slice? We show that if P (K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, including the tau and s-invariants, as well as suitably normalized d-invariants of Dehn surgeries on K. We also investigate the (2, 2l) cables P-l (K), and find obstructions to smooth concordance to the sum of the (2,2l) torus link and a split link.