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arXiv · 2312.08263

Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids

Marvin Dippell·David Kern
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Abstract

We present a framework for the reduction of various geometric structures extending the classical coisotropic Poisson reduction. For this we introduce constraint manifolds and constraint vector bundles. A constraint Serre-Swan theorem is proven, identifying constraint vector bundles with certain finitely generated projective modules, and a Cartan calculus for constraint differentiable forms and multivector fields is introduced. All of these constructions will be shown to be compatible with reduction. Finally, we apply this to obtain a reduction procedure for Lie (bi-)algebroids and Dirac manifolds.

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Marvin Dippell, David Kern. 2023-12-13. Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids. https://arxiv.org/abs/2312.08263

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