2024/08/12 by Nate Fisher, Fisher, Nate
Mathematics · #20F18 #20F65 #53C23 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2408.06510
openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study characteristics of horofunction boundaries of Carnot groups. In particular, we show that for Carnot groups, i.e., stratified nilpotent Lie groups equipped with certain left-invariant homogeneous metrics, all horofunctions are piecewise-defined using Pansu derivatives. For higher Heisenberg groups and filiform Lie groups, two families which generalize the standard 3-dimensional real Heisenberg group, we study the dimensions and topologies of their horofunction boundaries. In doing so, we find that filiform Lie groups of dimension n≥ 8 provide the first-known examples of Carnot groups G whose horofunction boundaries are not of dimension dim(G) - 1.