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The Topological Representation of Oriented Matroids

Abstract

We present a new proof of the 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 Schonflies 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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Correspondence to Jürgen Bokowski or Simon King or Susanne Mock or Ileana Streinu.

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Bokowski, J., King, S., Mock, S. et al. The Topological Representation of Oriented Matroids. Discrete Comput Geom 33, 645–668 (2005). https://doi.org/10.1007/s00454-005-1164-4

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Keywords

  • Computational Mathematic
  • Representation Theorem
  • General Rank
  • Topological Representation
  • Oriented Matroids