2024/03/05 by Daniel López García, Garcia, Daniel López, Nicolás Martínez Alba +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2403.03178
openalex publication_date 2024/03/05 · openalex created_date 2024/03/07 · openalex updated_date 2026/07/28
The Marsden-Weinstein-Meyer symplectic reduction has an analogous version for cosymplectic manifolds. In this paper we extend this cosymplectic reduction to the context of groupoids. Moreover, we prove how in the case of an algebroid associated to a cosymplectic groupoid, the integration commutes with the reduction (analogously to what happens in Poisson geometry). On the other hand, we show how the cosymplectic reduction of a groupoid induces a symplectic reduction on a canonical symplectic subgroupoid. Finally, we study what happens to the multiplicative Chern class associated with the S1-central extensions of the reduced groupoid.