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arXiv:math/0001129 [math.DG]AbstractReferencesReviewsResources

Connections in Poisson Geometry I: Holonomy and Invariants

Rui Loja Fernandes

Published 2000-01-24, updated 2000-02-04Version 2

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.

Comments: 40 pages; Final version (replaces preliminary version, several corrections made)
Categories: math.DG, math.SG
Subjects: 53D17, 53C05, 53C12
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