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Isometry groups of closed Lorentz 4-manifolds are Jordan

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Abstract

We prove that for any closed Lorentz 4-manifold (M, g) 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 \([\Gamma :A]\le C\).

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Notes

  1. Recall that a manifold is closed if it is compact and has no boundary.

  2. See e.g. Lemma 3.1 below for some references.

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Acknowledgements

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

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  1. Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain

    Ignasi Mundet i Riera

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  1. Ignasi Mundet i Riera
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Correspondence to Ignasi Mundet i Riera.

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This work has been partially supported by the (Spanish) MEC Project MTM2015-65361-P.

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Mundet i Riera, I. Isometry groups of closed Lorentz 4-manifolds are Jordan. Geom Dedicata 207, 201–207 (2020). https://doi.org/10.1007/s10711-019-00493-7

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