In a previous work it is shown that every finite group G of diffeomorphisms of a connected smooth manifold M of dimension $$\ge 2$$ ≥ 2 equals, up to quotient by the flow, the centralizer of the group of smooth automorphisms of a G -invariant complete vector field X (shortly X describes G ). Here the foregoing result is extended to show that every finite group of diffeomorphisms of M is described, within the group of all homeomorphisms of M , by a vector field. As a consequence, it is proved that a finite group of homeomorphisms of a compact connected topological 4-manifold, whose action is free, is described by a continuous flow.

中文翻译：

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微分同胚的有限群由向量场拓扑决定

在先前的工作中，表明维度 $$\ge 2$$ ≥ 2 的连通光滑流形 M 的微分同胚的每个有限群 G 等于，直到流的商，a 的光滑自同构群的中心化子G 不变的完全向量场 X（简称 X 描述 G ）。这里将上述结果推广到表明，在 M 的所有同胚群内，M 的每一个有限微分同胚群都由一个向量场描述。因此，证明了动作是自由的紧连通拓扑4-流形的有限同胚群是由连续流描述的。