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arXiv · 1407.3300

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

Marco Gualtieri·Songhao Li·Alvaro Pelayo·Tudor Ratiu
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Abstract

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.

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Marco Gualtieri, Songhao Li, Alvaro Pelayo, Tudor Ratiu. 2014-07-11. The tropical momentum map: a classification of toric log symplectic manifolds. https://arxiv.org/abs/1407.3300

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