Related papers: Contact toric manifolds

We characterize the actions of compact tori on smooth manifolds for which the orbit space is a topological manifold (either closed or with boundary). For closed manifolds the result was originally proved by Styrt in 2009. We give a new…

The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…

After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective action of a torus whose Reeb vector field corresponds to an element of the Lie algebra of the torus, we…

By studying completely integrable torus actions on contact manifolds we prove a conjecture of Toth and Zelditch that toric integrable geodesic flows on tori must have flat metrics.

In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical…

In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over…

We classify contact toric 3-manifolds up to contactomorphism, through explicit descriptions, building off of work by Lerman [Lerman03]. As an application, we classify all contact structures on 3-manifolds that can be realised as a concave…

The toric manifolds in question were invented by Bott and studied by Grossberg and Karshon under the name "Bott towers". Interest in them comes from their relation to characters of semisimple Lie groups and geometric quantization. We offer…

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold $S^2\times S^3$. In particular we give a…

We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…

We show that the cone associated with a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than…

Contact structures on 3-manifolds are analyzed by decomposing the manifold along convex surfaces. Background results of Giroux, Eliashberg, Colin, and Honda are discussed with an emphasis on examples. Convex decompositions are then used to…

Q-Gorenstein toric contact manifolds provide an interesting class of examples of contact manifolds with torsion first Chern class. They are completely determined by certain rational convex polytopes, called toric diagrams, and arise both as…

We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution. We prove a general Myers theorem and establish a Cartan-Hadamard result for almost qc-Einstein…

The aim of this paper is to address the following question: given a contact manifold $(\Sigma, \xi)$, what can be said about the aspherical symplectic manifolds $(W, \omega)$ bounded by $(\Sigma, \xi)$ ? We first extend a theorem of…

We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.

Let $M$ be a connected compact contact toric manifold. Most of such manifolds are of Reeb type. We show that if $M$ is of Reeb type, then $\pi_1(M)$ is finite cyclic, and we describe how to obtain the order of $\pi_1(M)$ from the moment map…

We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields…

Let $(M, \alpha)$ be a $2n+1$-dimensional connected compact contact toric manifold of Reeb type. Suppose the contact form $\alpha$ is regular, we find conditions under which $M$ is homeomorphic to $S^{2n+1}$.

The goal of this paper is to classify symplectic toric stratified spaces with isolated singularities. This extends a result of Burns, Guillemin, and Lerman which carries out this classification in the compact connected case. In making this…