Related papers: A long exact sequence on the composition of Dehn t…

We give an explicit description of the Floer cohomology of a family of Dehn twists about disjoint Lagrangian spheres in a w+ - monotone rational symplectic manifold. As a byproduct of our framework, in a monotone symplectic manifold we are…

The long exact sequence describes how the Floer cohomology of two Lagrangian submanifolds changes if one of them is modified by applying a Dehn twist. We give a proof in the simplest case (no bubbling). The paper contains a certain amount…

We study the Floer cohomology of the Dehn twist along a real Lagrangian sphere in a symplectic manifold endowed with an anti-symplectic involution. We prove that there exists a distinguished element in the Floer group that is a fixed point…

We use quilted Floer theory to generalize Seidel's long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply it to construct versions of the Floer and Khovanov-Rozansky exact triangles in Lagrangian Floer theory…

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…

In this paper, we generalize construction of Seidel's long exact sequence of Lagrangian Floer cohomology to that of compact Lagrangian submanifolds with vanishing Malsov class on general Calabi-Yau manifolds. We use the framework of…

We prove an isomorphism of Floer cohomologies under geometric composition of Lagrangian correspondences in exact and monotone settings.

We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of…

Let $(M^4,\omega)$ be a geometrically bounded symplectic manifold, and $L\subset M$ a Lagrangian nodal sphere such that $\omega\mid_{\pi_2(M,L)}=0$. We show that an equatorial Dehn twist of $L$ does not extend to a Hamiltonian…

The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain…

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 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 the following new ingredients: (1) rework on part of the Lagrangian surgery theory; (2) constructions of Lagrangian cobordisms on product symplectic manifolds; (3) extending Biran-Cornea Lagrangian cobordism…

We study Dehn--Seidel twists on configurations of Lagrangian spheres in symplectic $K3$ surfaces, using tools from Seiberg--Witten theory. In the case of $ADE$ configurations of Lagrangian spheres, we prove that a naturally associated…

Given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann…

We construct an analogue of Viterbo's transfer morphism for Floer homology of an automorphism of a Liouville domain. As an application we prove that the Dehn-Seidel twist along any Lagrangian sphere in a Liouville domain of dimension…

Let $M$ be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and $\phi$ be an exact symplectomorphism of $M$ which, near infinity, is equal to either the identity or the…

In this paper we establish a Floer-theoretical analog of the classical Gysin long exact sequence from algebraic topology for circle bundles. We study algebraic and functorial properties of this sequence and derive applications to…

For an adiscal or monotone regular coisotropic submanifold $N$ of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of $N$. Given a Hamiltonian isotopy $\phi=(\phi^t)$ and a…

We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give…