The reduced knot Floer complex

David Krcatovich

doi:10.1016/j.topol.2015.08.008

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arXiv · 1310.7624

The reduced knot Floer complex

David Krcatovich

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Abstract

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 of 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 Ozsv\'ath-Szab\'o $\tau$ invariant, the knot signature and the Rasmussen $s$ invariant.

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David Krcatovich. 2013-10-28. The reduced knot Floer complex. https://doi.org/10.1016/j.topol.2015.08.008

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