A Topological Representation Theorem for Oriented Matroids

Authors

Jürgen Bokowski, Technische Universitat Darmstadt
Simon King, Technische Universitat Darmstadt
Sussane Mock, Technische Universitat Darmstadt
Ileana Streinu, Smith CollegeFollow

Document Type

Article

Publication Date

4-2005

Publication Title

Discrete & Computational Geometry

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 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.

Keywords

oriented matroid, pseudosphere arrangement, chirotope, Lawrence representation, hyperline sequences, generalized Schönflies theorem

Volume

33

Issue

4

First Page

645

Last Page

668

DOI

dx.doi.org/10.1007/s00454-005-1164-4

ISSN

1432-0444

Comments

Author’s submitted manuscript. Published in Discrete & Computational Geometry under the title The Topological Representation of Oriented Matroids.

Recommended Citation

Bokowski, Jürgen; King, Simon; Mock, Sussane; and Streinu, Ileana, "A Topological Representation Theorem for Oriented Matroids" (2005). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/18