极小流的第一上同调群
First Cohomology Groups of Minimal Flows
摘要：
我们在这项工作中的兴趣是在小组的最小流量与紧阿贝尔群的纤维。我们从范畴和代数的角度研究了它们的结构，并描述了它们的动力学与一维代数-拓扑不变量的关系。本文确定了具有单连通作用群的流的第一上同调群和具有自由圈的拓扑自由流的第一上同调群。作为一个应用程序，我们表明，这些流的最小扩展不仅存在，但他们有一个丰富的代数结构。
英文摘要：
Our interest in this work is in group extensions of minimal flows with compact abelian groups in the fibres. We study their structure from categorical and algebraic points of view, and describe relations of their dynamics to the one-dimensional algebraic-topological invariants. We determine the first cohomology groups of flows with simply connected acting groups and those of topologically free flows possessing a free cycle. As an application we show that minimal extensions of these flows not only do exist, but they have a rich algebraic structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
