Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids
Differential Geometry
2023-12-14 v1 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2312.08263,
title = {Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids},
author = {Marvin Dippell and David Kern},
journal= {arXiv preprint arXiv:2312.08263},
year = {2023}
}
Comments
Comments are welcome! arXiv admin note: substantial text overlap with arXiv:2310.05613