Abstract
For any rank r oriented matroid M, a construction is given of a “topological representation” of M by an arrangement of homotopy spheres in a simplicial complex which is homotopy equivalent to S r–1. The construction is completely explicit and depends only on a choice of maximal flag in M. If M is orientable, then all Folkman-Lawrence representations of all orientations of M embed in this representation in a homotopically nice way.
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Anderson, L. Homotopy Sphere Representations for Matroids. Ann. Comb. 16, 189–202 (2012). https://doi.org/10.1007/s00026-012-0125-x
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DOI: https://doi.org/10.1007/s00026-012-0125-x