Reduction (by stages) in the whole Lagrange–Poincaré category

Abstract

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We study the reduction scheme in the whole category, introduced in to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category. Furthermore, we analyze the Noether theorem on -bundles, the relationship with Hamiltonian reduction by stages and some geometric aspects of the definition of this category.