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ISOMETRY GROUP OF LORENTZ MANIFOLDS: A COARSE PERSPECTIVE

Abstract : We prove a structure theorem for the isometry group Iso(M, g) of a compact Lorentz manifold, under the assumption that a closed subgroup has exponential growth. We don't assume anything about the identity component of Iso(M, g), so that our results apply for discrete isometry groups. We infer a full classification of lattices that can act isometrically on compact Lorentz manifolds. Moreover, without any growth hypothesis, we prove a Tits alternative for discrete subgroups of Iso(M, g).
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03143447
Contributor : Charles Frances <>
Submitted on : Wednesday, February 17, 2021 - 2:12:59 PM
Last modification on : Friday, February 19, 2021 - 3:24:21 AM

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  • HAL Id : hal-03143447, version 1
  • ARXIV : 2102.09213

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Charles Frances. ISOMETRY GROUP OF LORENTZ MANIFOLDS: A COARSE PERSPECTIVE. 2021. ⟨hal-03143447⟩

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