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 journalArticlepeer-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 languageEnglish
Pages (from-to)343-361
Number of pages19
JournalJournal of Geometric Mechanics
Volume12
Issue number3
DOIs
StatePublished - 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

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