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

Abstract

In this work one shows that given a connected $C^{\infty }$-manifold $M$ of dimension $\ge 2$ 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 $X$.

13 pages, no figures

References in corpus (1)

• Every finite group is the group of self homotopy equivalences of an elliptic space