Toric Actions on b-Symplectic Manifolds

By V. Guillemin, Eva Miranda, A. R. Pires, G. Scott. 2013

70 citations recorded by the source corpus.

We study Hamiltonian actions on b-symplectic manifolds with a focus on the e ective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classi es these manifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus. At the end of the paper we suggest further avenues of study, including an example of a toric action on a b 2-manifold and applications of our ideas to integrable systems on b-manifolds

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b82708a9274c1539573709317b99d5c9d3486ea

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In Geometry and Topology

1. Tudor S. Ratiu
2. Songhao Li
3. 'Alvaro Pelayo
4. M. Gualtieri
5. Anna Fino
6. G. Cavalcanti
7. D. Waldram
8. M. Graña

In Mathematical Physics

1. Tudor S. Ratiu
2. Songhao Li
3. 'Alvaro Pelayo
4. M. Gualtieri
5. Anna Fino
6. G. Cavalcanti
7. D. Waldram
8. O. Hohm

Citations in the corpus

• The tropical momentum map: a classification of toric log symplectic manifolds (2014, background): “logarithmic symplectic forms, in a way which is particularly useful in guiding intuition. The study of toric log symplectic manifolds was initiated in the paper of Guillemin, Miranda, Pires and Scott [8], who focused on the case where the degeneracy locus Z⊂Mof the Poisson structure is a smooth hype”