Regular poisson manifolds of compact types

Marius Crainic, Rui Loja Fernandes, David Martínez Torres

Research output: Contribution to journalArticlepeer-review


This is the second manuscript of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this manuscript, 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 aWeyl 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).

Original languageEnglish (US)
Pages (from-to)1-166
Number of pages166
StatePublished - 2019


  • Integral affine structure
  • Poisson manifold
  • Symplectic gerbe
  • Symplectic groupoid

ASJC Scopus subject areas

  • General Mathematics


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