Algebraic definition of Holonomy on Poisson Manifold
Zakaria Giunashvili
TL;DR
This paper introduces an algebraic approach to defining connections and linearized holonomy on symplectic leaves within Poisson manifolds, advancing the mathematical framework for understanding their geometric structure.
Contribution
It provides a novel algebraic construction of connections on symplectic leaves, enabling the definition of linearized holonomy on regular symplectic foliations.
Findings
Algebraic construction of connections on symplectic leaves
Definition of linearized holonomy for regular symplectic foliations
Extension of geometric concepts to algebraic frameworks
Abstract
We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in \cite{Ginzburg}. This construction is suitable for the definition of the linearized holonomy on a regular symplectic foliation.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Geometry and complex manifolds