A counterexample to the extension space conjecture for realizable oriented matroids

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


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

Upcoming Events of This Seminar