Finite $C^\infty$-actions are described by one vector field

Details Finite $C^\infty$-actions are described by one vector field Finite $C^\infty$-actions are described by one vector field

2011-12-13

arxiv.org/abs/1112.2881v1

Mathematics

Differential Geometry

13 pages, no figures

Scientific paper

In this work one shows that given a connected $C^\infty$-manifold $M$ of
dimension $\geq 2$ and a finite subgroup $G\subset \Diff(M)$, 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 $X$.

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