THE METHOD of AVERAGING for POISSON CONNECTIONS on FOLIATIONS and ITS APPLICATIONS

Misael Avendanõ-Camacho; Isaac Hasse-Armengol; Eduardo Velasco-Barreras; Yury Vorobiev

doi:10.3934/jgm.2020015

THE METHOD of AVERAGING for POISSON CONNECTIONS on FOLIATIONS and ITS APPLICATIONS

Misael Avendanõ-Camacho, Isaac Hasse-Armengol, Eduardo Velasco-Barreras, Yury Vorobiev

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

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Resumen

On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.

Idioma original	Inglés
Páginas (desde-hasta)	343-361
Número de páginas	19
Publicación	Journal of Geometric Mechanics
Volumen	12
N.º	3
DOI	https://doi.org/10.3934/jgm.2020015
Estado	Publicada - 1 sep. 2020

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abstract = "On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.",

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AU - Avendanõ-Camacho, Misael

AU - Hasse-Armengol, Isaac

AU - Velasco-Barreras, Eduardo

AU - Vorobiev, Yury

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.

AB - On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.

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KW - Cotangential group action

KW - Dirac structure

KW - Invariant ehresmann connections

KW - Poisson foliation

KW - Pre-momentum map

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JO - Journal of Geometric Mechanics

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THE METHOD of AVERAGING for POISSON CONNECTIONS on FOLIATIONS and ITS APPLICATIONS

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