相关论文: Traceless Character Varieties, the Link Surgeries …

We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M,\omega) which upon passing to homology yields ring isomorphisms with the big quantum…

We prove that the unreduced singular instanton homology $I^\sharp(Y,K;\mathbb{Z})$ has $2$-torsion for any null-homologous fibered knot $K$ of genus $g>0$ in a closed $3$-manifold $Y$ except for $\#^{2g}S^1\times S^2$. The main technical…

We prove the existence of an exact triangle for the Pin(2)-monopole Floer homology groups of three manifolds related by specific Dehn surgeries on a given knot. Unlike the counterpart in usual monopole Floer homology, only two of the three…

We study the interplay between hyperbolic geometry and monopole Floer homology for a closed oriented three-manifold $Y$ with $b_1=1$ equipped with a torsion spin$^c$ structure $\mathfrak{s}$. We show that, under favorable circumstances, one…

Given a link $L$, Dowlin constructed a filtered complex inducing a spectral sequence with $E_2$-page isomorphic to the Khovanov homology $\overline{Kh}(L)$ and $E_\infty$-page isomorphic to the knot Floer homology $\widehat{HFK}(m(L))$ of…

We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of…

Let $(M,\omega)$ be a symplectic manifold compact or convex at infinity. Consider a closed Lagrangian submanifold $L$ such that $\omega |_{\pi_2(M,L)}=0$ and $\mu|_{\pi_2(M,L)}=0$, where $\mu$ is the Maslov index. Given any Lagrangian…

This is a companion paper to an earlier work of the authors. In this paper, we provide an axiomatic definition of Floer homology for balanced sutured manifolds and prove that the graded Euler characteristic $\chi_{\rm gr}$ of this homology…

Heegaard Floer homology and knot Floer homology are powerful invariants of 3-manifolds and links respectively. L-space knots are knots which admit Dehn surgeries to 3-manifolds with Heegaard Floer homology of minimal rank. In this paper we…

Seidel-Smith and Hendricks used equivariant Floer cohomology to define some spectral sequences from symplectic Khovanov homology and Heegaard Floer homology. These spectral sequences give rise to Smith-type inequalities. Similar-looking…

We show that if $Y$ is the boundary of an almost-rational plumbing, then the framed instanton Floer homology $\smash{I^\#(Y)}$ is isomorphic to the Heegaard Floer homology $\smash{\widehat{\mathit{HF}}(Y; \mathbb{C})}$. This class of…

We provide a unified framework for proving Reidemeister-invariance and functoriality for a wide range of link homology theories. These include Lee homology, Heegaard Floer homology of branched double covers, singular instanton homology, and…

Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S^3 and the Heegaard Floer homology of its double-branched cover. This…

An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying $d$-invariant inequalities…

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…

Lattice cohomology, defined by N\'emethi in (arXiv:0709.0841), is an invariant of negative definite plumbed 3-manifolds which conjecturally computes the Heegaard Floer homology HF^+. We prove a surgery exact triangle for the lattice…

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…

In this paper we introduce a chain complex $C_{1 \pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of…

The goal of this paper is twofold: (i) define a symplectic Khovanov type homology for a transverse link in a fibered closed $3$-manifold $M$ (with an auxiliary choice of a homotopy class of loops that intersect each fiber once) and (ii)…

We establish a relationship between the sheaf-theoretic SL(2,C) Floer cohomology HP(Y), as defined by Abouzaid and Manolescu, for Y a surgery on a small knot in S^3, and the SL(2,C) Casson invariant, as defined by Curtis. We determine a…