Contact Toric Manifolds

By Eugene Lerman. 2001

198 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0986ec725243d4d5028973ab82628d327bbc256a

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In Geometry and Topology

1. J. Sparks
2. D. Martelli
3. A. Hanany
4. Alberto Zaffaroni
5. Craig van Coevering
6. Shing-Tung Yau
7. S. Franco
8. J. Gauntlett

Citations in the corpus

• Examples of asymptotically conical Ricci-flat Kähler manifolds (2008, background): “which from [39] is a strictly convex rational polyhedral cone.”
• The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005, methodology): “2 The symplectic toric cones that are not of Reeb type are rather uninteresting: they are either cones over S2 × S1, cones over principle T3 bundles over S2, or cones over products Tm × Sm+2 j−1, m > 1, j ≥ 0 [27].”
• Sasaki-Einstein Manifolds (2010, background): “(Toric symplectic cones with Reeb vector fields not satisfying this condition form a short list and have been classified [66].”
• Gauge theories from toric geometry and brane tilings (2005, background): “Y is smooth if and only if the polyhedral cone is good [51], although we will not enter into the general details of this here — see, for example, [46].”
• Ricci-flat Kähler metrics on crepant resolutions of Kähler cones (2008, background): “We have the moment cone defined by (48) C(μ) := μ(C(S)) ∪ {o}, which from [27] is a strictly convex rational polyhedral cone.”
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds (2006, background): “Like the Kähler-Ricci flow [13], the long-time existence can be also proved.”
• Toric Sasaki-Einstein metrics on S2 × S3 (2004, background): “From the Delzant theorem in [ 13 ] it follows that, for a, b, c relatively prime, the Sasaki–Einstein metrics La,b,c are equivariantly contactomorphic to the”
• Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals (2004, methodology): “of compact manifolds [36, 37, 21] is rather standard in symplectic geometry, but the generalisation for orbifolds [38], and especially cones [35, 20], is quite recent.”