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Title:
A counterexample to the extension space conjecture for realizable oriented matroids
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Abstract:
The extension space conjecture, proposed by Sturmfels and Ziegler in 1993, is a conjecture about the topology of a realizable oriented matroid's "extension space", which is a topological model for the set of all extensions of the oriented matroid by a single element. Equivalently, it is a conjecture about the poset of proper zonotopal tilings of a zonotope, namely that this poset is homotopy equivalent to a sphere. In this talk we describe a counterexample to this conjecture in three dimensions.
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