2007/10/30 by Luca Stefanini, Stefanini, Luca
Mathematics · Medicine · #18D05 (Secondary) #53D20 (Primary) #58H05 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:18D05 #msc:53D20 #msc:58H05
paper · pdf · doi:10.48550/arxiv.0710.5753
20 pages, corrected misspellt preposition in the title
openalex publication_date 2007/10/30 · arxiv created 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G^⋆ we obtain a suitably connected integrating symplectic double groupoid \calS. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold P can be integrated to a Poisson action of the symplectic groupoid \poidd\calSG^⋆ on the symplectic groupoid for P. Finally, we show that the quotient Poisson manifold P/G is also integrable, giving an explicit construction of a symplectic groupoid for it, by a reduction procedure on an associated morphism of double Lie groupoids.