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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	343-361
Number of pages	19
Journal	Journal of Geometric Mechanics
Volume	12
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2020015
State	Published - 1 Sep 2020

Bibliographical note

Funding Information:
70G45. Key words and phrases. Poisson foliation, cotangential group action, invariant Ehresmann connections, averaging method, pre-momentum map, Dirac structure . The authors are supported by CONACYT grant CB2015 no. 258302. E. Velasco - Barreras was supported by FAPERJ grants E-26/202.411/2019 and E-26/202.412/2019. ∗ Corresponding author: Misael Avendaño-Camacho.

Publisher Copyright:
© American Institute of Mathematical Sciences.

Keywords

Averaging method
Cotangential group action
Dirac structure
Invariant ehresmann connections
Poisson foliation
Pre-momentum map

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AU - Vorobiev, Yury

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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

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KW - Invariant ehresmann connections

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KW - Pre-momentum map

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

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Keywords

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