on the trefoil is the lens space, $L(5,4)$, and thus the $(p,q)$ cable of the trefoil admits L-space surgeries whenever $q\ge p+1$. In particular, the Floer homology of the $(2,3)$ cable of the trefoil is determined by its Alexander polynomial which, from Equation is $$(t-1+t^{-1})(t^2-1+t^{-2})= t^{3}-t^{2}+1-t^{-2}+t^{-4}.$$ On the other hand, this is the same Alexander polynomial as that of the $(3,4)$ torus knot. As this knot also admits lens space surgeries, we find that the two distinct knots have identical Floer invariants. This example was obtained by a rather lengthy calculation in [@MyThesis].

We find this example noteworthy as it appears difficult to produce families of L-space knots with the same Floer invariants. On the other hand, we will show in an upcoming paper that infinite families of knots with identical Floer invariants are rather abundant. These families, however, do not admit L-space surgeries. It would be interesting to probe Theorem \[thm:lspace\] for further examples of L-space knots with identical Floer homology.

[**[Remarks:]{}**]{} Versions of  Theorems \[thm:filt\] and \[thm:tau\] appear in the author’s dissertation, [@MyThesis].

[**[Acknowledgment:]{}**]{} I wish to thank Peter Ozsv[á]{}th for his advice and encouragement throughout my time as a graduate student, in which the heart of this 