Separable and tree-like asymptotic cones of groups

2010/10/06 by Alessandro Sisto, Sisto, Alessandro · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Graph theory and applications #Group Theory (math.GR) #Logic (math.LO) #Metric Geometry (math.MG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1010.1199

openalex publication_date 2010/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using methods from nonstandard analysis, we will discuss which metric spaces can be realized as asymptotic cones. Applying the results we will find in the context of groups, we will prove that a group with "a few" separable asymptotic cones is virtually nilpotent, and we will classify the real trees appearing as asymptotic cones of (not necessarily hyperbolic) groups.

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