Séminaire Lotharingien de Combinatoire, 78B.31 (2017), 7 pp.

Gaku Liu

A Counterexample to the Extension Space Conjecture for Realizable Oriented Matroids

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.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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