2009/02/13 by Stuart Armstrong, Armstrong, Stuart, Jussi Westergren +1
Computer Science · Mathematics · #52B20 #81T25 #83C27 #83C47 #FOS: Mathematics #Geometric Topology (math.GT) #Graph theory and applications #Metric Geometry (math.MG) #Topological and Geometric Data Analysis #advanced mathematical theories #math.GT #math.MG #msc:52B20 #msc:81T25 #msc:83C27 #msc:83C47
paper · pdf · doi:10.48550/arxiv.0902.2301
arxiv created 2009/02/13 · openalex publication_date 2009/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric and the dimension of the holonomy group. If the holonomy group is of dimension one and the metric is positive-definite, a single type of directed edges is needed.