Hierarchy for groups acting on hyperbolic Zⁿ-spaces

2016/11/01 by Andrei-Paul Grecianu, Grecianu, Andrei-Paul, Alexei Myasnikov +3
Computer Science · Mathematics · #05E18 #20F65 (Primary) 20E08 #20F67 #53C23 (Secondary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1611.00314

openalex publication_date 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In their first article, the authors initiated a systematic study of hyperbolic Λ-metric spaces, where Λ is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case Λ= Zⁿ taken with the right lexicographic order and studies the structure of finitely generated groups acting on hyperbolic Zⁿ-metric spaces. Under certain constraints, the structure of such groups is described in terms of a \em hierarchy similar to the one established for Zⁿ-free groups by Kharlampovich, Myasnikov, Remeslennikov and Serbin.

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