Topological Representations of Matroids and the cd-index
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A fundamental achievement in the theory of matroids is the Topological Representation Theorem which says that every oriented matroid arises from an arrangement of pseudospheres. In 2003 Swartz extended this result to arbitrary matroids by using homotopy spheres. Later, Anderson and Engstrom also constructed topological representations of matroids by homotopy sphere arrangements. Inspired by Swartz's work, this thesis will show an explicit fully partitioned homotopy sphere
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Connelly, Robert