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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