2002/09/26 by Juergen Bokowski, Bokowski, Juergen, Simon King +5
Computer Science · Mathematics · #52C40 (Primary) 57N50 #57N45 (Secondary) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis #math.CO #math.GT #msc:52C40 #msc:57N45 #msc:57N50
paper · pdf · doi:10.48550/arxiv.math/0209364
21 pages, 4 figures
arxiv created 2002/09/26 · openalex publication_date 2002/09/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Schönflies theorem. As an application, we show that one can read off oriented matroids from arrangements of embedded spheres of codimension one, even if wild spheres are involved.