Related papers: Link Floer homology and the Thurston norm
Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots in the three-sphere, which takes values in link Floer homology. This invariant can be used to also construct an invariant of transverse…
In this article we define and compute the Novikov Floer homology associated to a non-resonant magnetic field and a mechanical Hamiltonian on a flat torus T^{2N}. As a result, we deduce that this Hamiltonian system always has 2N+1…
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 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…
An explicit polynomial in the linking numbers $l_{ij}$ and Milnor's triple linking numbers $\mu(rst)$ on six component links is shown to be a well-defined finite type link-homotopy invariant. This solves a problem raised by B. Mellor and D.…
We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose…
In this paper, a relationship between the determinant of an alternating link and a certain polytope obtained from the link diagram is analyzed. We also show that when the underlying graph of the link diagram is properly oriented, the number…
We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes…
We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which help to compute their Floer homology. The…
We give an algorithm for computing the knot Floer homology of a $ (1,1) $ knot from a particular presentation of its fundamental group.
In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere with the sign assignment coming from a coherent system of orientations on Whitney…
Inspired by the $S^n$ colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of link Floer homology with infinite full twists.…
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 a number of fundamental properties about instanton knot Floer homology. Our arguments rely on general properties of sutured Floer theories and apply also in the Heegaard Floer and monopole Floer settings, where many of our results…
In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homology and real sutured Heegaard Floer…
The Floer homology of (RP^n,T^n) is calculated, for n odd.
For closed 3-manifolds, Heegaard Floer homology is related to the Thurston norm through results due to Ozsv\'ath and Szab\'o, Ni, and Hedden. For example, given a closed 3-manifold Y, there is a bijection between vertices of the HF^+(Y)…
In this paper, we compute the symplectic Floer homology of the figure eight knot. This provides first nontrivial knot with trivial symplectic Floer homology.
We introduce a simple combinatorial method for computing all versions of the knot Floer homology of the preimage of a two-bridge knot K(p,q) inside its double-branched cover, -L(p,q). The 4-pointed genus 1 Heegaard diagram we obtain looks…
In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic…