JournalsrmiVol. 37, No. 3pp. 1207–1224

The geometry of EE-manifolds

  • Eva Miranda

    Universitat Politècnica de Catalunya, Barcelona, Spain and Sorbonne Université, Paris, France
  • Geoffrey Scott

    University of Toronto, Canada
The geometry of $E$-manifolds cover
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Abstract

Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called an EE-tangent bundle) which is particularly well-suited to the study of singular differential forms and their cohomology. This setting generalizes bb-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. We generalize Moser’s theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. We give applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.

Cite this article

Eva Miranda, Geoffrey Scott, The geometry of EE-manifolds. Rev. Mat. Iberoam. 37 (2021), no. 3, pp. 1207–1224

DOI 10.4171/RMI/1232