Related papers: Holomorphic disks and link invariants

We present several expected properties of the holomorphic Floer theory of a holomorphic symplectic manifold. In particular, we propose a conjecture relating holomorphic Floer theory of Hitchin integrable systems and Donaldson-Thomas…

We give a short introduction to the contact invariant in bordered Floer homology defined by F\"oldv\'ari, Hendricks, and the authors. The construction relies on a special class of foliated open books. We discuss a procedure to obtain such a…

Inspired by the Ozsv\'ath-Szab\'o mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $\Phi_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using the cobordism maps on involutive…

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of…

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some…

The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles…

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups…

Given an l-component pointed oriented link (L,p) in an oriented three-manifold Y, one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F_2[U_1,...,U_l]. Moving the basepoint p_i in the link component L_i once…

We define a 1-parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda-Przytycki-Sikora (arxiv:0409414) and the invariant defined by Winkeler (arxiv:2106.03834). The new…

We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected…

We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes…

Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this…

A natural family of potentially 2-torsion elements in the integer homology cobordism group consists of splices of knots with their mirrors. We show that such 3-manifolds have locally trivial involutive Floer homology. We show some related…

We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives…

We define an invariant of based transverse links, as a well-defined element inside the equivariant Heegaard Floer cohomology of its branched double cover, defined by Lipschitz, Hendricks, and Sarkar. We prove the naturality and…

This article is a standalone introduction to sutured Floer homology for graduate students in geometry and topology. It is divided into three parts. The first part is an introductory level exposition of Lagrangian Floer homology. The second…

We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they…

This is the third of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three…

Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this…