A Topological Representation Theorem for Oriented Matroids
Combinatorics
2007-05-23 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0209364,
title = {A Topological Representation Theorem for Oriented Matroids},
author = {Juergen Bokowski and Simon King and Susanne Mock and Ileana Streinu},
journal= {arXiv preprint arXiv:math/0209364},
year = {2007}
}
Comments
21 pages, 4 figures