Stability of higher order singular points of poisson manifolds and Lie algebroids

Jean Paul Dufour, Aïssa Wade

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular points of order k ≥ 1 for Poisson structures and Lie algebroids. Finally, we apply our results to pre-symplectic leaves of Dirac manifolds.

Original languageEnglish (US)
Pages (from-to)545-559
Number of pages15
JournalAnnales de l'Institut Fourier
Volume56
Issue number3
DOIs
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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