Zusammenfassung für den Vortrag am 16.01.2018 (11:00 Uhr)Seminar on Nonlinear Algebra
Gaku Liu (MPI MIS, Leipzig)
A counterexample to the extension space conjecture for realizable oriented matroids
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.