The reduced knot Floer complex.

We define a “reduced” version of the knot Floer complex CFK − ( K ) , and show that it behaves well under connected sums and retains enough information to compute Heegaard Floer d -invariants of manifolds arising as surgeries on the knot K . As an application to connected sums, we prove that if a knot in the three-sphere admits an L -space surgery, it must be a prime knot. As an application to the computation of d -invariants, we show that the Alexander polynomial is a concordance invariant within the class of L -space knots, and show the four-genus bound given by the d -invariant of +1-surgery is independent of the genus bounds given by the Ozsváth–Szabó τ invariant, the knot signature and the Rasmussen s invariant. [ABSTRACT FROM AUTHOR]