Concordance properties of parallel links Daniel RubermanSaso Strle 57M2557Q60concordance of linkssplit links 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 $(2,2\ell)$ cables $P_{\ell}(K)$, and find obstructions to smooth concordance to the sum of the $(2,2\ell)$ torus link and a split link. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4982 10.1512/iumj.2013.62.4982 en Indiana Univ. Math. J. 62 (2013) 799 - 814 state-of-the-art mathematics http://iumj.org/access/