Related papers: Corrigendum to "Knot Floer homology detects fibred…

Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$…

Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai's theory of sutured manifold decomposition and contact topology. We implement this strategy for…

This note corrects the mistakes in the splicing formulas of the paper "Floer homology and splicing knot complements". The mistakes are the result of the incorrect assumption that for a knot $K$ inside a homology sphere $Y$, the involution…

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of…

We define Floer homology theories for oriented, singular knots in S^3 and show that one of these theories can be defined combinatorially for planar singular knots.

We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in \cite{li} naturally admits an integer graded lifting, and it formulates a filtration and induced…

We prove that the Knot Floer homology group of a fibred knot of genus g in the Alexander grading 1-g is isomorphic to a version of the fixed point Floer homology of an area-preserving representative of the monodromy.

A companion paper to "On knot Floer homology in branched double covers" applied to braided branched loci. We reprove the main result of that paper concerning alternating branched loci when projected to an annulus, without using Khovanov…

Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a certain three-manifold invariant, Heegaard Floer homology,…

We say that a given knot $J\subset S^3$ is detected by its knot Floer homology and $A$-polynomial if whenever a knot $K\subset S^3$ has the same knot Floer homology and the same $A$-polynomial as $J$, then $K=J$. In this paper we show that…

Extensive rewrite. Tables and proofs have been reformatted and/or rewritten for clarity.

We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, $T(2,6)$, $T(3,3)$, $L7n1$, and the link $T(2,2n)$ with the orientation of…

We give an obstruction to unknotting a knot by adding a twisted band, derived from Heegaard Floer homology.

This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories and give some examples which illustrate a somewhat mysterious correspondence…

We apply sutured Floer homology techniques to study the knot and link Floer homologies of various links with annuli embedded in their exteriors. Our main results include, for large $m$, characterizations of links with the same link Floer…

Ozsvath and Szabo proved that knot Floer homology determines the genera of knots in S^3. We will generalize this deep result to links in homology 3-spheres, by adapting their method. Our proof relies on a result of Gabai and some…

We give a precise description of splicing formulas from a previous paper in terms of knot Floer complex associated with a knot in homology sphere.

We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots, and that HOMFLY homology detects infinitely many such knots; these theories were previously known to detect a mere six knots, all…

We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.

Knot Floer homology is a knot invariant defined using holomorphic curves. In more recent work, taking cues from bordered Floer homology,the authors described another knot invariant, called "bordered knot Floer homology", which has an…