Related papers: Symplectic Convexity for Orbifolds

Given a symplectic manifold, we ask in how many different ways can a torus act on it. Classification theorems in equivariant symplectic geometry can sometimes tell that two Hamiltonian torus actions are inequivalent, but often they do not…

The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the group of bundle automorphism on this space. Since, in…

Let $G$ be a compact and connected Lie group. The Hamiltonian $G$-model functor maps the category of symplectic representations of closed subgroups of $G$ to the category of exact Hamiltonian $G$-actions. Based on previous joint work with…

In the paper we describe obstructions for the existence of symplectic and Hamiltonian symplectic circle actions on closed compact manifolds in terms of Hirzebruch genera and relations between differential and homotopic invariants of such…

We outline the construction of invariants of Hamiltonian group actions on symplectic manifolds. These invariants can be viewed as an equivariant version of Gromov-Witten invariants. They are derived from solutions of a PDE involving the…

A convexity theorem for certain G-orbits in a complexified Riemannian symmetric space G_C/K_C is proved. Applications to analytically continued spherical functions will be given.

In this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action $\Phi$ of the multiplicative group $G = \mathbb{R}^+$ on exact symplectic manifolds $(M, \omega,\theta)$, with $\omega =…

We study the extension of homologically trivial symplectic or Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic $4$-manifolds. On one hand, we construct symplectic involutions on minimal irrational…

In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…

A natural way of generalising Hamiltonian toric manifolds is to permit the presence of generic isolated singularities for the moment map. For a class of such ``almost-toric 4-manifolds'' which admits a Hamiltonian $S^1$-action we show that…

We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian…

We consider symplectic manifolds with Hamiltonian torus actions which are "almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants…

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…

A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We…

By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.

We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly supported, provided one uses the correct local system of…

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…