The reduced knot Floer complex

By David Krcatovich. 2013

49 citations recorded by the source corpus.

We define a “reduced” version of the knot Floer complex CFK − (K) 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 Ozsvath–Szabo τ invariant, the knot signature and the Rasmussen s invariant.

Subfields: Genetics, Geometry and Topology, Neurology

View Paper: https://www.semanticscholar.org/paper/aa5cf317274a72ee4ee79c1b60d1828625a7d49e

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In Genetics

1. John A. Baldwin
2. Steven Sivek
3. J. Greene

In Geometry and Topology

1. John A. Baldwin
2. Steven Sivek
3. J. Greene

In Neurology

1. John A. Baldwin
2. Steven Sivek
3. J. Greene

Citations in the corpus

• Khovanov homology detects the trefoils (2018, background): “10 can be used to give new proofs that the dimension of ĤFK detects the trefoil [HW14] and that L-space knots are prime [Krc15].”