Connections in Poisson Geometry I: Holonomy and Invariants
Rui Loja Fernandes
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.
Create a lesson
Related papers
The Bernstein problem in higher dimensional Heisenberg groups
Gianmarco Giovannardi, Simone Verzellesi
A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture
Yuan Liao, Ziyang Qin, Jui-Hui Chung et al.
A counterexample to Nirenberg's conjecture on closed asymptotic curves
Harrison Banks, Mohammad Ghomi, Hongda Qiu et al.
Topping's conjecture for solutions of harmonic map flow with isolated bubbles
Melanie Rupflin, Alex Waldron, Sebastian Woodward
The Renormalized Area--Willmore Relation
Alvaro Pampano, Aaron J. Tyrrell
Compact lcK manifolds with Gauduchon parallel vector fields
Andrei Moroianu, Giacomo Perri