IUMJ

Title: Concordance properties of parallel links

Authors: Daniel Ruberman and Saso Strle

Issue: Volume 62 (2013), Issue 3, 799-814

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 $(2,2\ell)$ cables $P_{\ell}(K)$, and find obstructions to smooth concordance to the sum of the $(2,2\ell)$ torus link and a split link.