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Poisson geometry around Poisson submanifolds

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arxiv 2205.11457 v2 pith:FNOFECU4 submitted 2022-05-23 math.SG math.DG

Rui Loja Fernandes , Ioan Marcut This is my paper · ORCID
classification math.SGmath.DG
keywords poissonaroundgroupoidlinearizationlocalmodelsubmanifoldssymplectic
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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.

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  1. Fundamentals of Lie categories and Yang-Mills theory for multiplicative Ehresmann connections

    math.DG 2025-07 conditional novelty 7.0 of 10

    Multiplicative Ehresmann connections on general Lie algebroids yield a gauge-invariant pair of Yang-Mills equations that reduce to the classical equation in the transitive case.

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