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

By M. Gualtieri, Songhao Li, 'Alvaro Pelayo, Tudor S. Ratiu. 2014

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cbe3356261d4fe726bc87982561913df8bc8e6a8