using other satellite operations or asking for more refined concordance information (see, for instance, [@Doubling; @LN2008]). One can also ask the question where $s(K)$ is replaced by $\tau(K)$ (or any other smooth concordance invariant). The results of the present paper, together with further expected TQFT properties of  Floer homology lead us to conjecture that in this case the answer is “no".

In a related direction, we point out that the $(p,1)$ cabling operation $\phi_{p,1}$ was studied in detail by Kawauchi in [@Kawauchi1980]. He showed that $\phi_{p,1}$ is a homomorphism from the algebraic concordance group to itself, and remarked that it does not appear to be so on the level of the (smooth) concordance group in general (see the parenthetical remark at the end of the proof of Proposition $4.1$ of [@Kawauchi1980]). Using Theorem \[thm:tau\] we are able to prove that this is so.

\[cor:concordance\] Let $\mathcal{C}$ denote the smooth concordance group, and let $$\phi_{p,1}: \mathcal{C}\rightarrow \mathcal{C}$$ denote the map defined by $\phi_{p,1}([K])=[K_{p,1}]$. Then $\phi_{p,1}$ is not a homomorphism for any $p$

### Cable knots and complex curves

 Let $V_f$ be a complex curve $$V_f=\{ (z,w)\in \C^2| 0=f(z,w)\in \mathbb{C}[z,w]\},$$ and let $$S^3=\{(z,w)\subset \mathbb{C}^2| |z|^2+|w|^2=1\}$$ be the three-sphere. Further suppose that $$K=V_f 