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arXiv · 1606.05033

A counterexample to the extension space conjecture for realizable oriented matroids

Gaku Liu
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Abstract

The extension space conjecture of oriented matroid theory states that the space of all one-element, non-loop, non-coloop extensions of a realizable oriented matroid of rank $d$ has the homotopy type of a sphere of dimension $d-1$. We disprove this conjecture by showing the existence of a realizable uniform oriented matroid of high rank and corank 3 with disconnected extension space.

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Gaku Liu. 2016-07-17. A counterexample to the extension space conjecture for realizable oriented matroids. https://doi.org/10.1112/jlms.12264

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