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Published online by Cambridge University Press: 04 June 2025
The chapters provides a survey on the topology of various posets of oriented matroids analogous to various topological spaces, including extension spaces, combinatorial Grassmannians, and combinatorial flag spaces. A general framework for interpreting maps from spaces to posets is laid down, by way of McCord’s Theorem and the Semi-algebraic Triangulation Theorem. The chapter includes a discussion of the (now-disproved) extension space conjecture and of the various results on the topology of the MacPhersonian.
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