相关论文: Corrigendum to "Knot Floer homology detects fibred…

This note corrects an erroneous statement in Lemma 3.8 of the author's paper Embedded Contact Homology and Seiberg-Witten Floer Homology IV which was published in Volume 14 of Geometry and Topology in 2009.

In this paper we find a family of knots with trivial Alexander polynomial, and construct two non-isotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study the sutured Floer homology invariants of…

Given an equivariant knot $K$ of order $2$, we study the induced action of the symmetry on the knot Floer homology. We relate this action with the induced action of the symmetry on the Heegaard Floer homology of large surgeries on $K$. This…

In the early days of the Floer theory, Atiyah asked if there is a Milnor fiber description of the Floer homology of the links of singularities. We answer this question for the Brieskorn-Hamm complete intersection singularities. The…

We exhibit the first example of a knot in the three-sphere with a pair of minimal genus Seifert surfaces that can be distinguished using the sutured Floer homology of their complementary manifolds together with the Spin^c-grading. This…

We correct a mistake regarding almost complex structures on Hilbert schemes of points in surfaces in arXiv:1510.02449. The error does not affect the main results of the paper, and only affects the proofs of invariance of equivariant…

We define a homological action on sutured instanton Floer homology. This action is well-defined up to scalars, and behaves well under connected sums and sutured manifold decompositions. As an application, we show that instanton knot…

By proving a connected sum formula for the Legendrian invariant $\lambda_+$ in knot Floer homology we exhibit infinitely many transversely non simple knots.

We give a new, conceptually simpler proof of the fact that knots in $S^3$ with positive L-space surgeries are fibered and strongly quasipositive. Our motivation for doing so is that this new proof uses comparatively little Heegaard…

We construct $S^r$-colored knot Floer homologies and prove that they satisfy categorified recurrence relations. The associated Euler characteristic implies $q$-holonomicity of the corresponding sequence of colored Alexander polynomials, in…

Let $K$ be a rationally null-homologous knot in a three-manifold $Y$. We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold obtained as Morse surgery on the knot…

This paper has been withdrawn due to an error in the proof. The paper implicitly assumed that every homotopically trivial knot is related to the unknot by negative crossings, which is false (as was pointed out to the author by Peter…

We derive a new exact sequence in the hat-version of Heegaard Floer homology. As a consequence we see a functorial connection between the invariant of Legendrian knots and the contact element. As an application we derive two vanishing…

We show that if K is a non-trivial knot inside a homology sphere X, the rank of the knot Floer homology group associated with K is strictly bigger than the rank of the Heegaard Floer homology group associated with X.

We define sutured Heegaard diagrams for null-homologous knots in 3-manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a…

Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a…

Using the Bordered Floer theory of Lipshitz-Ozsv\'ath-Thurston we prove that the $(p,q)$-cables of any non-trivial knots are not Heegaard Floer homologically thin. Using the proof and a theorem of Zemke, we find a larger set of satellite…

We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…

We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and…

We propose a framework for unifying the sl(N) Khovanov-Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply graded homology theory which categorifies the HOMFLY…