Isometry Group of Lorentz Manifolds: A Coarse Perspective

2021/02/18 by Frances, Charles
#Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2102.09213

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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