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arXiv · 1603.00064

Regular Poisson manifolds of compact types (PMCT 2)

Marius Crainic·Rui Loja Fernandes·David Martinez-Torres
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Abstract

This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine orbifolds. We prove that the cohomology class of the leafwise symplectic form varies linearly and that there is a distinguished polynomial function describing the leafwise sympletic volume. The leaf space of a PMCT carries a natural Duistermaat-Heckman measure and a Weyl type integration formula holds. We introduce the notion of a symplectic gerbe, and we show that they obstruct realizing PMCTs as the base of a symplectic complete isotropic fibration (a.k.a. a non-commutative integrable system).

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Marius Crainic, Rui Loja Fernandes, David Martinez-Torres. 2016-02-29. Regular Poisson manifolds of compact types (PMCT 2). https://arxiv.org/abs/1603.00064

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