English

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.

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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