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Hyperbolic actions of higher-rank lattices come from rank-one factors

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arxiv 2206.06431 v2 pith:ZNXYGXMT submitted 2022-06-13 math.GR

Uri Bader , Pierre-Emmanuel Caprace , Alex Furman , Alessandro Sisto This is my paper · ORCID
classification math.GR
keywords actionshyperboliccomefactorslatticesrank-onegammahigher
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abstract

We study actions of higher rank lattices $\Gamma<G$ on hyperbolic spaces, and we show that all such actions satisfying mild properties come from the rank-one factors of $G$. In particular, all non-elementary actions on an unbounded hyperbolic space are of this type.

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  1. Classifying group actions on hyperbolic spaces

    math.GR 2025-04 accept novelty 8.0 of 10

    For every countable weakly hyperbolic group, classifying general type actions on hyperbolic spaces is either smooth (isotropic case) or E_Kσ complete (anisotropic case), and all complexity levels are realized.

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