Chi Ho Yuen:Filtrations of tope spaces of oriented matroids

Abstract: Oriented matroids are matroids with extra sign data, and they arise naturally in the study of real hyperplane arrangements. In order to study the topology of real algebraic/tropical hypersurfaces constructed from patchworking, Renaudineau and Shaw introduced an algebraically defined filtration of the tope spaces of oriented matroids based on Quillen filtration, We will prove the equivalence of their filtration and the topologically defined Kalinin filtration, as well as the combinatorially defined Gelfand-Varchenko dual degree filtration. If time permits, we will also discuss a potential globalization. This is joint work with Kris Shaw.

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