标题： 非交换可积系统的全局作用量-角度变量 显示英文标题

标题： Global Action-Angle Variables for Non-Commutative Integrable Systems

摘要： 在本文中，我们分析了在泊松流形上正规非交换可积系统（NCI系统）存在全局作用角变量的障碍。 与局部作用角变量不同，只要此类可积系统的动量映射的纤维是紧致的，局部作用角变量就存在，而全局作用角变量很少存在。 这一事实最早由杜斯特马特在辛流形上的刘维尔可积系统情况下观察并分析，后来由达佐德-德尔赞在辛流形上的非交换可积系统情况下进行分析。 在我们更一般的情况下，相空间是一个任意的泊松流形，正如我们将通过抽象和具体例子所展示的，存在更多的障碍。 我们的方法利用了一些我们引入的新特性：NCI系统的动作丛和动作格子丛（这些丛是规范定义的）以及三个叶状结构（动作叶状结构、角度叶状结构和横截叶状结构），它们的存在也受到障碍的影响，通常具有上同调性质。 显示英文摘要

摘要： In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In contrast with local action-angle variables, which exist as soon as the fibers of the momentum map of such an integrable system are compact, global action-angle variables rarely exist. This fact was first observed and analyzed by Duistermaat in the case of Liouville integrable systems on symplectic manifolds and later by Dazord-Delzant in the case of non-commutative integrable systems on symplectic manifolds. In our more general case where phase space is an arbitrary Poisson manifold, there are more obstructions, as we will show both abstractly and on concrete examples. Our approach makes use of a few new features which we introduce: the action bundle and the action lattice bundle of the NCI system (these bundles are canonically defined) and three foliations (the action, angle and transverse foliation), whose existence is also subject to obstructions, often of a cohomological nature.