Related papers: Floer homology on the extended moduli space

We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and four-manifolds with boundary. We then…

Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_*(\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and…

In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading.…

We develop a new approach to Lagrangian-Floer gluing. The construction of the gluing map is based on the intersection theory in some Hilbert manifold of paths $\mathcal{P} $. We consider some moduli spaces of perturbed holomorphic curves…

We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced…

We use monopole Floer homology to study the topology of the space of contact structures on a 3-manifold. Our main tool is a generalisation of the Kronheimer--Mrowka--Ozsv\'ath--Szab\'o contact invariant to an invariant for families of…

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…

We derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangian fillings. More precisely, we show that such a concordance induces an isomorphism on the level of…

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein…

This article provides the first extension of Lagrangian Intersection Floer cohomology to Poisson structures which are almost everywhere symplectic, but degenerate on a lowerdimensional submanifold. The main result of the article is the…

Assume $M$ to be $\mathbb R^2$ or a closed surface of genus $g \geq 1$ and $\omega$ a symplectic form on $M$. Let $\varphi: M \to M$ be a symplectomorphism with hyperbolic fixed point $x$ and transversely intersecting stable and unstable…

We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix…

This paper studies the self-Floer theory of a monotone Lagrangian submanifold $L$ of a symplectic manifold $X$ in the presence of various kinds of symmetry. First we suppose $L$ is $K$-homogeneous and compute the image of low codimension…

Real Heegaard Floer homology is an invariant associated to a three-manifold equipped with an involution with nonempty fixed set of codimension two. We show that when the image of the fixed point set is nullhomologous in the quotient, the…

We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that…

Seiberg-Witten (Floer) theory, Ozsvath-Szabo's Heegaard Floer theory, Hutchings's embedded contact homology, in different stages of development, define (or are expected to define) packages of invariants for 3- and 4-manifolds (including…

Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized…

Giroux has described a correspondence between open book decompositions on a 3--manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book…

On one side, from the properties of Floer cohomology, invariant associated to a symplectic manifold, we define and study a notion of symplectic hyperbolicity and a symplectic capacity measuring it. On the other side, the usual notions of…

We prove the existence of a spectral sequence for Lagrangian Floer homology which converges to the Floer homology of the image of a Lagrangian submanifold under multiple fibred Dehn twists. The $E_1$ term of the sequence is given by the…