Connections in Poisson Geometry I: Holonomy and Invariants

2000/01/24 by Rui Loja Fernandes, Fernandes, Rui Loja · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.DG #math.SG #msc:53C05 #msc:53C12 #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0001129

40 pages; Final version (replaces preliminary version, several corrections made)

arxiv created 2000/02/04 · arxiv updated 2009/11/30

Abstract

We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by Izu 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.

Cited by

• Poisson triple systems
• Atiyah constructions for Lie algebroid connections on fiber bundles

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