Return to Colloquia & Seminar listing

### A counterexample to the extension space conjecture for realizable oriented matroids

**Algebra & Discrete Mathematics**

Speaker: | Gaku Liu, MIT |

Related Webpage: | https://arxiv.org/abs/1606.05033 |

Location: | 1147 MSB |

Start time: | Mon, Oct 31 2016, 4:10PM |

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 focus on the connection of this problem with polytopes and tilings of polytopes; no knowledge of matroids or oriented matroids is required.