Revista Matemática Iberoamericana

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Volume 30, Issue 1, 2014, pp. 317–330
DOI: 10.4171/RMI/780

Published online: 2014-03-23

Finite $C^{\infty}$-actions are described by a single vector field

Francisco Javier Turiel[1] and Antonio Viruel[2]

(1) Universidad de Málaga, Spain
(2) Universidad de Málaga, Spain

In this work it is shown that given a connected $C^{\infty}$-manifold $M$ of dimension $\geq 2$ and a finite subgroup $G\subset \operatorname{Diff}(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\times \mathbb{R}$, where the factor $\mathbb{R}$ comes from the flow of $X$.

Keywords: Finite group, group action, vector field

Turiel Francisco Javier, Viruel Antonio: Finite $C^{\infty}$-actions are described by a single vector field. Rev. Mat. Iberoam. 30 (2014), 317-330. doi: 10.4171/RMI/780