A Topological Representation Theorem for Oriented Matroids
  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 Sch{\"o}nflies 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. 
Juergen Bokowski, Simon King, Susanne Mock, Ileana Streinu