Homotopy sphere representations for matroids

2009/03/16 by Laura Anderson, Anderson, Laura
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:05B35 #msc:52B40

paper · pdf · doi:10.48550/arxiv.0903.2773

arxiv created 2009/03/16 · arxiv updated 2009/12/01

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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