Isometry groups of closed Lorentz 4-manifolds are Jordan

Abstract

We prove that for any closed Lorentz $4$-manifold $(M,g)$ the isometry group $Isom(M,g)$ is Jordan. Namely, there exists a constant $C$ (depending on $M$ and $g$) such that any finite subgroup $\Gamma \le Isom(M,g)$ has an abelian subgroup $A\le \Gamma$ satisfying $[\Gamma :A]\le C$.

7 pages, comments welcome

References in corpus (2)

• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
• Non Jordan groups of diffeomorphisms and actions of compact Lie groups on manifolds