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arXiv · 1811.05840

Finite groups of diffeomorphisms are topologically determined by a vector field

F. J. Turiel·A. Viruel
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Abstract

In a previous work it is shown that every finite group $G$ of diffeomorphisms of a connected smooth manifold $M$ of dimension $\geq 2$ 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.

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F. J. Turiel, A. Viruel. 2018-11-14. Finite groups of diffeomorphisms are topologically determined by a vector field. https://arxiv.org/abs/1811.05840

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