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Isometry groups of closed Lorentz 4-manifolds are Jordan

  • Ignasi Mundet i RieraEmail author
Original Paper
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Abstract

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

Keywords

Closed Lorentz manifolds Finite groups of isometries Jordan property 

Mathematics Subject Classification

57S17 54H15 53C50 

Notes

Acknowledgements

I wish to thank V. Popov for some corrections and useful comments on this paper.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Facultat de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain

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