obtained by Dehn surgery on $K$ (see [@Knots; @IntegerSurgeries; @RationalSurgeries]). In the case that surgery on $K$ yields a manifold with particularly simple Floer homology, this relationship tightly constrains the knot Floer homology invariants. The knot Floer homology, in turn, determine various geometric and topological properties of the knot e.g. the genus, fiberedness.

The three-manifolds with simplest Floer homology are the rational homology spheres, $Y$, for which the rank of the Floer homology is equal to the order of the first (singular) homology, i.e. rk$\ \HFa(Y) = |H_1(Y;\Z)|$. These manifolds are called [*L-spaces*]{}, and the name stems from the fact that lens spaces are L-spaces. In the case that positive surgery on $K$ yields an L-space, we call $K$ an [*L-space knot*]{}.  show that the knot Floer homology invariants of L-space knots are determined by the Alexander polynomial [@Lens]. In particular, a corollary of their theorem is that the coefficients of the Alexander polynomial of an L-space knot are all $\pm 1$, and that the knot must be fibered [@Ghiggini2007; @NiFibered] with four-genus equal to the Seifert genus [@FourBall]. Combining Theorem \[thm:tau\] with their result yields the following obstruction to a cable knot admitting an L-space surgery.

\[cor:cor2\] Suppose that 