Related papers: Equivariant Lagrangian displacements

We find general non-linear lagrangians of a U(1) field invariant under electric-magnetic duality. They are characterized by an arbitrary function and go to the Maxwell theory in the weak field limit. We give some explicit examples which are…

We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative…

Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^*M$, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain ergodic invariant Lagrangian graphs within a given…

We establish a new version of Floer homology for monotone Lagrangian submanifolds and apply it to prove the following (generalized) version of Audin's conjecture : if $L$ is an aspherical manifold which admits a monotone Lagrangian…

Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study…

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…

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…

We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstruction to displaceability of Lagrangians in the symplectic…

We use quasimap Floer cohomology for varying symplectic quotients to resolve several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an {\em open} subset of…

We use a new variational method --based on the theory of anti-selfdual Lagrangians developed in [2] and [3]-- to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in $\R^{2N}$.…

Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…

We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms. In addition these quasimorphisms are Lipschitz in the Hofer…

This paper classifies separated bounding pairs for Lagrangian submanifolds that are homologically trivial inside the ambient space, under the assumption that restriction on cohomology from the ambient space to the Lagrangian is surjective.…

We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given $N \ge 3$ and $R$ a connective $\mathbb E_1$-ring spectrum, there is a…

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…

We study the compact monotone Fukaya category of $T^*S^n$, for $n\geq 2$, and show that it is split-generated by two classes of objects: the zero-section $S^n$ (equipped with suitable bounding cochains) and a 1-parameter family of monotone…

\noindent Let $M\to N$ (resp.\ $C\to N$) be the fibre bundle of pseudo-Riemannian metrics of a given signature (resp.\ the bundle of linear connections) on an orientable connected manifold $N$. A geometrically defined class of first-order…

The theorem of Chekhanov asserts that a Lagrangian submanifold L has positive displacement energy under natural assumptions on the symplectic topology at infinity. It is greater than or equal to the minimal area of holomorphic disks bounded…

For G a Lie group acting on a symplectic manifold $(M,\omega)$ preserving a pair of Lagrangians $L_0$, $L_1$, under certain hypotheses not including equivariant transversality we construct a G-equivariant Floer cohomology of $L_0$ and…