Discrete & Computational Geometry
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.
oriented matroid, pseudosphere arrangement, chirotope, Lawrence representation, hyperline sequences, generalized Schönflies theorem
Bokowski, Jürgen; King, Simon; Mock, Sussane; and Streinu, Ileana, "A Topological Representation Theorem for Oriented Matroids" (2005). Faculty Publications. Paper 18.