The tropical momentum map: a classification of toric log symplectic manifolds

Friday, 11 July, 2014

Published in: 

arXiv:1407.3300

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization of affine space called a log affine manifold. Using this momentum map, we obtain a complete classification of such manifolds in terms of decorated log affine polytopes, hence extending the classification of symplectic toric manifolds achieved by Atiyah, Guillemin-Sternberg, Kostant, and Delzant.

Author(s): 

Marco Gualtieri
Songhao Li
Alvaro Pelayo
Tudor Ratiu