标题： 流体涡旋中同调的作用 I：非相对论性流动 显示英文标题

标题： The role of homology in fluid vortices I: non-relativistic flow

摘要： 奇异同调和德拉姆同调与上同调的方法被回顾，以适用于涡旋的结构和运动。 特别是，它们首先被应用于积分不变量的概念。 在简要回顾流体力学的基本要素后，用外微分形式和同调理论的语言表达时，涡旋理论的基本定律被显示为根植于积分不变量同调理论的陈述。 显示英文摘要

摘要： The methods of singular and de Rham homology and cohomology are reviewed to the extent that they are applicable to the structure and motion of vortices. In particular, they are first applied to the concept of integral invariants. After a brief review of the elements of fluid mechanics, when expressed in the language of exterior differential forms and homology theory, the basic laws of vortex theory are shown to be statements that are rooted in the homology theory of integral invariants.