Related papers: Floer lasagna modules from link Floer homology
We study the Floer-theoretic interaction between disjointly supported Hamiltonians by comparing Floer-theoretic invariants of these Hamiltonians with the ones of their sum. These invariants include spectral invariants, boundary depth and…
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,…
Given a link in the three-sphere, Ozsv\'ath and Szab\'o showed that there is a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its branched double cover. The aim of this paper…
Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques. In…
We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators…
We use Liu-Tian's virtual moduli cycle methods to construct detailedly the explicit isomorphism between Floer homology and quantum homology for any closed symplectic manifold that was first outlined by Piunikhin, Salamon and Schwarz for the…
There is a generalization of Heegaard-Floer theory from ${\mathfrak{gl}}_{1|1}$ to other Lie (super)algebras $^L{\mathfrak{g}}$. The corresponding category of A-branes is solvable explicitly and categorifies quantum $U_q(^L{\mathfrak{g}})$…
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…
In this paper we outline a program for the classification of Floer-type theories, (or defining invariants of finite type for families). We consider Khovanov complexes as a local system on the space of knots introduced by V. Vassiliev and…
Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey…
Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define new knot invariants and apply them to deduce novel linear…
We prove an isomorphism of Floer cohomologies under geometric composition of Lagrangian correspondences in exact and monotone settings.
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…
In 1985 lectures at MSRI, A. Casson introduced an interesting integer valued invariant for any oriented integral homology 3-sphere Y via beautiful constructions on representation spaces (see [1] for an exposition). The Casson invariant…
We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the holomorphic disk Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants,…
These notes are adapted from two talks given at the 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology at the Alfred Renyi Institute. We will quickly review what we do and do not know about the…
This paper is a short introduction to the combinatorial version of tangle Floer homology defined in "Combinatorial tangle Floer homology". There are two equivalent definitions---one in terms of strand diagrams, and one in terms of bordered…
Viewing the BRAID invariant as a generator of link Floer homology we generalise work of Baldwin-Vela-Vick to obtain rank bounds on the next to top grading of knot Floer homology. These allow us to classify links with knot Floer homology of…
In this paper, we focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. We collect such manifolds systematically by using the smoothing order on links.
Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle…