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A counterexample to the extension space conjecture for realizable oriented matroids

  • Gaku Liu (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)

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. The talk will not assume any prior knowledge of oriented matroids.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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