Related papers: A self-pairing theorem for tangle Floer homology

Tensoring finite pointed simplicial sets with commutative ring spectra yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions…

Let $G$ be a group with a finite balanced presentation $P$. We associate a Heegaard Floer homology group $\widehat{HF}_P(G)$ with the pair $(G,P)$ based on some extra choices and technical assumptions. We show that $\widehat{HF}_P(G)$ is…

We establish a criterion on wrapped Floer homology of an exact Lagrangian sub- manifold in a Liouville domain, which ensures the almost-existence of Hamiltonian chords near a given energy level. To this purpose we introduce a relative…

We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology concordances induce split…

Suppose an amenable group $G$ is acting freely on a simply connected simplicial complex $\tilde X$ with compact quotient $X$. Fix $n \geq 1$, assume $H_n(\tilde X, \mathbb{Z})=0$ and let $(H_i)$ be a Farber chain in $G$. We prove that the…

We define band maps in unoriented link Floer homology and show that they form an unoriented skein exact triangle. These band maps are similar to the band maps in equivariant Khovanov homology given by the Lee deformation. As a key tool, we…

This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If $M$ is such a manifold, we show that the type D structure $\widehat{\mathit{CFD}}$ may be viewed as a set of immersed…

Motivated by various possible generalizations of Taubes's \(SW=Gr\) theorem [T] to Floer-theoretic setting, we prove certain variants of Taubes's convergence theorem in \cite{T} (the first part of his proof of \(SW=Gr\)). In place of the…

Analogous to a recent result of N. Kowalzig and U. Kr\"{a}hmer for twisted Calabi-Yau algebras, we show that the Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra, thus…

This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In…

We define Hamiltonian Floer homology with differential graded (DG) local coefficients for symplectically aspherical manifolds. The differential of the underlying complex involves chain representatives of the fundamental classes of the…

We give some new link detection results for link Floer homology, Khovanov homology and annular Khovanov homology. The links we detect arise via different closure operations on $3$-braids. Examples of our results include that link Floer…

With a 4-ended tangle $T$, we associate a Heegaard Floer invariant $\operatorname{CFT^\partial}(T)$, the peculiar module of $T$. Based on Zarev's bordered sutured Heegaard Floer theory, we prove a glueing formula for this invariant which…

Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t_0 on Sigma(L), the 2-fold cover of S^3 branched along L. We prove, generalizing results of Manolescu-Owens and…

We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a construction which is more amenable to computation and easier…

Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensional cobordisms. Bordered Heegaard Floer homology…

We compute the Lagrangian Floer cohomology groups of certain tori in closed simply connected symplectic 4-manifolds arising from Fintushel-Stern knot surgery. These manifolds are usually not symplectically aspherical. As a result of the…

By analyzing the decategorification of bordered sutured Heegaard Floer homology, we reinterpret and generalize the classical Frohman-Nicas TQFT for the Alexander polynomial in the setting of 3d sutured cobordisms between sutured surfaces.…

We show that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. This allows us to define the symmetric Hochschild cohomology of twisted group algebras,…

We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in $S^3$ and the involutive bordered Heegaard Floer theory of its complement determine each other. In particular, given two knots…