A counterexample to the extension space conjecture for realizable oriented matroids
Combinatorics
2019-08-14 v2
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 has the homotopy type of a sphere of dimension . We disprove this conjecture by showing the existence of a realizable uniform oriented matroid of high rank and corank 3 with disconnected extension space.
Cite
@article{arxiv.1606.05033,
title = {A counterexample to the extension space conjecture for realizable oriented matroids},
author = {Gaku Liu},
journal= {arXiv preprint arXiv:1606.05033},
year = {2019}
}
Comments
23 pages. v2: Revised introduction, corrected statement of Proposition 3.3, other minor edits