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

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arxiv 2312.08263 v1 pith:OKXU2FAW submitted 2023-12-13 math.DG math.SG

Marvin Dippell , David Kern This is my paper · ORCID
classification math.DGmath.SG
keywords constraintreductionbundlesvectoralgebroidsmanifoldsapplycalculus
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Infinitesimal Star Products Compatible with Coisotropic Reduction

    math.QA 2025-01 conditional novelty 7.0 of 10

    Infinitesimal reduction-compatible star products are exactly bivector fields plus symmetric differential operators built from the characteristic distribution and the normal bundle, up to constraint equivalence.

  2. Multisymplectic observable reduction using constraint triples

    math.SG 2025-05 conditional novelty 6.0 of 10

    Any BV-module with a cocycle yields an L∞-algebra of observables, and constraint-triple reduction of that algebra recovers and explains the multisymplectic reduction of Blacker, Miti and Ryvkin.

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