Hamiltonian group actions on exact symplectic manifolds with proper momentum maps are standard

TL;DR

This paper characterizes Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps, showing they are globally linearizable in certain cases, thus extending understanding of symplectic symmetry structures.

Contribution

It provides a complete classification of such Hamiltonian actions and proves linearizability for actions on contractible manifolds with proper momentum maps.

Findings

Hamiltonian actions are fully characterized under the given conditions.

Actions on contractible manifolds are globally linearizable.

The results extend the understanding of symplectic group actions.

Abstract

We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold with a proper momentum map is globally linearizable.