On symplectic lifts of actions for complete Lagrangian fibrations
Juan Carlos Marrero, Edith Padr\'on
TL;DR
This paper investigates how group actions can be symplectically lifted in the context of complete Lagrangian fibrations, extending the understanding of cotangent lifts via cohomology and exploring generalizations.
Contribution
It provides a cohomological description of symplectic cotangent lifts and extends the framework to general complete Lagrangian fibrations.
Findings
Cohomological characterization of cotangent lifts
Extension of lifts to complete Lagrangian fibrations
Framework for symplectic lifts in fibrations
Abstract
In this note we discuss symplectic lifts of actions for a complete Lagrangian fibration. Firstly, we describe the symplectic cotangent lifts of a G-action on a manifold Q in terms of 1-cocycles in the cohomology of G induced by the action with values in the space of closed 1-forms on Q. After this, we consider the general case of complete Lagrangian fibrations.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology