The modular class of a Poisson map

2011/03/22 by Raquel Caseiro, Rui Loja Fernandes, Caseiro, Raquel +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1103.4305

Final version accepted for publication in Annales de l'Institut Fourier. Several changes made to the manuscript, based on referees' remarks

openalex publication_date 2011/03/22 · arxiv created 2012/08/03 · arxiv updated 2012/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.

Citations

• Lectures on Integrability of Lie Brackets
• The Symplectization Functor

Related

• The modular class of a regular Poisson manifold and the Reeb invariant of its symplectic foliation
• The modular class of a twisted Poisson structure
• Holonomy on Poisson Manifolds and the Modular Class
• The homology class of a Poisson transversal
• Poisson cohomology of a class of log symplectic manifolds