Connections in poisson geometry I: Holonomy and invariants

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We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by I. Vaisman. We show that these connections play an important role in the study of global properties of Poisson manifolds and we use them to define Poisson holonomy and new invariants of Poisson manifolds.

Original languageEnglish (US)
Pages (from-to)303-365
Number of pages63
JournalJournal of Differential Geometry
Issue number2
StatePublished - 2000
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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