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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