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

1 Scopus citations

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

Publisher Copyright:
© American Institute of Mathematical Sciences.

Keywords

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

Access to Document

10.3934/jgm.2020015

Cite this

@article{7abe969b228142128ba408eeb86d3dd9,

title = "THE METHOD of AVERAGING for POISSON CONNECTIONS on FOLIATIONS and ITS APPLICATIONS",

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.",

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

author = "Misael Avendan{\~o}-Camacho and Isaac Hasse-Armengol and Eduardo Velasco-Barreras and Yury Vorobiev",

note = "Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences.",

year = "2020",

month = sep,

day = "1",

doi = "10.3934/jgm.2020015",

language = "Ingl{\'e}s",

volume = "12",

pages = "343--361",

journal = "Journal of Geometric Mechanics",

issn = "1941-4889",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - THE METHOD of AVERAGING for POISSON CONNECTIONS on FOLIATIONS and ITS APPLICATIONS

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.

KW - Averaging method

KW - Cotangential group action

KW - Dirac structure

KW - Invariant ehresmann connections

KW - Poisson foliation

KW - Pre-momentum map

UR - http://www.scopus.com/inward/record.url?scp=85092785110&partnerID=8YFLogxK

U2 - 10.3934/jgm.2020015

DO - 10.3934/jgm.2020015

M3 - Artículo

AN - SCOPUS:85092785110

SN - 1941-4889

VL - 12

SP - 343

EP - 361

JO - Journal of Geometric Mechanics

JF - Journal of Geometric Mechanics

IS - 3

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this