Almost toric symplectic four-manifolds
By N. Leung, Margaret Symington. 2003
112 citations recorded by the source corpus.
Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space of the spherical pendulum and rational balls useful for symplectic surgeries. The main result of the paper is a complete classification up to diffeomorphism of closed almost toric four-manifolds. A key step in the proof is a geometric classification of the singular affine structures that can occur on the base of a closed almost toric four-manifold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dd023828468b655b92d4797225a8e1e5b49fe8be
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- D. Matessi
- Renato Vianna
- Ricardo Casta no Bernard
- Mark Gross
- Valentino Tosatti
- B. Weinkove
- K. Fukaya
- Michael T. Anderson
In Geometry and Topology
- D. Matessi
- Ricardo Casta no Bernard
- Renato Vianna
- Mark Gross
- Bernd S Siebert
- P. Hacking
- M. Abouzaid
- S. Keel
Citations in the corpus
- Infinitely many exotic monotone Lagrangian tori in ℂℙ2 (2014, methodology): “For a detailed account on almost toric fibrations we refer the reader to the work of Symington [14] and Leung-Symington [12].”
- Lagrangian 3-torus fibrations (2006, background): “Our construction of Lagrangian fibrations has a flavor similar to the work on almost toric symplectic geometry of Leung and Symington [24].”
- Toric degenerations and Batyrev-Borisov duality (2004, background): “as an exercise a construction of an example of such; for a hint, either study carefully the construction above or consult [11].”
- Infinitely many monotone Lagrangian tori in del Pezzo surfaces (2016, methodology): “The idea is to construct different almost toric fibrations (denoted from here by ATF) [23,31] of CP2.”
- Symplectic theory of completely integrable Hamiltonian systems (2011, unknown): “These structures have been studied in the context of integrable systems (in particular by Nguyên Tiên Zung [115]), but they also became a central concept in the works by Symington [100] and Symington and Leung [71] in the context of symplectic geometry and topology, and by Gross and Siebert [52, 53,”