Contact Toric Manifolds

@article{Lerman2001ContactTM,
  title={Contact Toric Manifolds},
  author={Eugene Lerman},
  journal={Journal of Symplectic Geometry},
  year={2001},
  volume={1},
  pages={785-828}
}
  • E. Lerman
  • Published 1 July 2001
  • Mathematics
  • Journal of Symplectic Geometry
We complete the classification of compact connected contact toric manifolds initiated by Banyaga and Molino and by Galicki and Boyer. As an application we prove the conjectures of Toth and Zelditch on toric integrable systems on the n-torus and the 2-sphere. 
Toric contact geometry in arbitrary codimension
We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the DelzantExpand
Toric Integrable Metrics on Tori Are Flat
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.
Homotopy groups of K-contact toric manifolds
Contact toric manifolds of Reeb type are a subclass of contact toric manifolds which have the property that they are classified by the images of the associated moment maps. We compute their first andExpand
Toric actions in cosymplectic geometry
Abstract We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
Categories of symplectic toric manifolds as Picard stack torsors
We outline a proof that the stack of symplectic toric G-manifolds over a fixed orbit space W is a torsor for the stack of symplectic toric G-principal bundles over W.
And Related Manifolds
We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on T ×S and certain related 5-manifolds. These structures occur inExpand
Equivariant Cohomological Rigidity of Topological Contact Toric Manifolds
We introduce the category of topological contact toric manifolds which is a topological generalization of compact connected contact toric manifolds, and study their basic properties. Our main theoremExpand
Toric integrable geodesic flows
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.
LCK metrics on toric LCS manifolds
Abstract We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs ( C , a ) , where C is a good cone inExpand
Homotopy groups of K-contact toric manifold
We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
Toric integrable geodesic flows
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.
Contact cuts
We describe a contact analog of the symplectic cut construction [L]. As an application we show that the group of contactomorphisms for certain overtwisted contact structures on lens spaces containsExpand
A note on toric contact geometry
Abstract After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective torus action whose Reeb vector field corresponds to anExpand
A convexity theorem for torus actions on contact manifolds
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 providedExpand
Symplectic toric orbifolds
A symplectic toric orbifold is a compact connected orbifold $M$, a symplectic form $\omega$ on $M$, and an effective Hamiltonian action of a torus $T$ on $M$, where the dimension of $T$ is half theExpand
Une structure de contact, même tendue, est plus ou moins tordue
This paper proves thé existence of non isomorphic tight contact structures on T. It aiso shows that ail Lagrangian incompressible embedded tori in T x (R^^O}) are homotopic.
Symplectic Techniques in Physics
Preface 1. Introduction 2. The geometry of the moment map 3. Motion in a Yang-Mills field and the principle of general covariance 4. Complete integrability 5. Contractions of symplectic homogeneousExpand
Le thorme de rduction de Marsden-Weinstein en gomtrie cosymplectique et de contact
Abstract We show that the classical Marsden-Weinstein Reduction theorem for Hamiltonian systems with symmetries is still true for contact manifolds and cosympletic manifolds (i.e. canonical manifoldsExpand
THE GEOMETRY SURROUNDING THE ARNOLD-LIOUVILLE THEOREM
We explain how a generalized completely integrable hamil­ tonian system on a symplectic manifold (M, f2) can be viewed as a generalized Duistermaat fibration: i.e. a fibration 7r : M2n -+ wn of aExpand
Examples for obstructions to action-angle coordinates
On donne des exemples de varietes symplectiques qui sont aussi des fibres toriques principaux avec des fibres lagrangiennes. Ces fibres sont des exemples d'espaces avec une obstruction a l'existenceExpand
...
1
2
...