A Topological Representation Theorem for Oriented Matroids

Details A Topological Representation Theorem for Oriented Matroids A Topological Representation Theorem for Oriented Matroids

2002-09-26

arxiv.org/abs/math/0209364v1

Mathematics

Combinatorics

21 pages, 4 figures

Scientific paper

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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