We define a “reduced” version of the knot Floer complex CFK-(K), and show that itbehaves well under connected sums and retains enough information to compute HeegaardFloer d-invariants of manifolds arising as surgeries on the knot K. As an application toconnected sums, we prove that if a knot in the three-sphere admits an L-space surgery, itmust be a prime knot. As an application to the computation of d-invariants, we show thatthe Alexander polynomial is a concordance invariant within the class of L-space knots, andshow the four-genus bound given by the d-invariant of +1-surgery is independent of the genusbounds given by the Ozsvath-Szabo τ invariant, the knot signature and the Rasmussen sinvariant.
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