Poisson geometry around Poisson submanifolds

2022/05/23 by Fernandes, Rui Loja, Marcut, Ioan · 3 citations
#53D17 #58H05 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2205.11457

Abstract

We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases all the known linearization theorems for fixed points and symplectic leaves. The symplectic groupoid version of these results gives a solution to the groupoid coisotropic embedding problem.

Cited by

• Slices for reductive group actions in algebraic and holomorphic symplectic geometry
• Analytic Linearization and Holomorphic Extensions of Proper Groupoids
• Jacobi Hamiltonian Integrators

Related

• Normal forms in Poisson geometry
• Normal forms for Poisson maps and symplectic groupoids around Poisson\n transversals
• The Poisson saturation of coregular submanifolds
• Nonlinearizability of certain Poisson structures near a symplectic leaf
• Normal forms for principal Poisson Hamiltonian spaces