\HFa(-Y)$. In this case $\tau_\alpha(Y,K)$ provides upper bounds for the classical framing invariants of Legendrian and transverse representatives of $K$ in the contact structure $\xi$. Indeed, using our present results, Theorem $1.4$ of [@tbbounds] was able to provide the first systematic construction of prime knot types in many tight contact structures whose classical framing invariants are constrained to be arbitrarily negative.

Geometric Consequences
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In addition to the theory of Legendrian knots and the connection with the four-ball genus, the Floer invariants of cable knots can be used in several other contexts. We take some time to discuss these results.

### Concordance information

It is straightforward to see that cabling induces a well-defined operation on the smooth concordance group, $\mathcal{C}$. Indeed, if $K$ and $J$ are concordant, their $(p,q)$ cables will be concordant via a concordance which “follows along" the concordance between $K$ and $J$ (see, for instance, [@Kawauchi1980] for more details). Thus cabling defines a sequence of maps: $$\phi_{p,q}: \mathcal{C}\rightarrow \mathcal{C},$$ where $\phi_{p,q}([K])=[K_{p,q}]$ (here $[K]$ denotes the smooth concordance class of $K$). By pre-composing with $\phi_{p,q}$, it follows that any smooth concordance invariant provides a sequence of smooth concordance invariants. In the present context, we obtain functions $$\ctau{n}:= \tau 