Connections in Poisson Geometry I: Holonomy and Invariants

Details Connections in Poisson Geometry I: Holonomy and Invariants Connections in Poisson Geometry I: Holonomy and Invariants

2000-01-24

arxiv.org/abs/math/0001129v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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