fiber surface of an iterated cable of the unknot is isotopic to a piece of a complex curve if and only if all the cabling coefficients are positive.

Note the lack of restriction on $q$. We also remark that the “if" direction of the theorem holds for the class of knots which bound [*quasipositive Seifert surfaces*]{}. Quasipositive Seifert surfaces are those which can be obtained from parallel disks by attaching bands with a positive half twist (see Figure $1$ of [@ComplexCable]). We postpone the proof of Theorem \[thm:ComplexCable\] until [@ComplexCable]. There, we determines the relationship between the contact structure associated to a fibered knot and those associated to its cables. Theorem \[thm:ComplexCable\] is a corollary of this relationship and of a connection between contact geometry and the knot theory of complex curves established in [@SQPfiber; @Rudolph2005].

### Cable knots and lens space (L-space) surgeries

One area of low-dimensional topology where the  invariants have had a significant impact is in the study of Dehn surgery [@BGH; @Ghiggini2007; @LensMe; @NiFibered; @Lens; @AbsGrad; @Figure8; @RasGoda; @Ras2007; @Wang2006]. Many of these results draw on the close relationship between the knot Floer homology invariants of a knot, $K$, and the   invariants of the closed three-manifolds 