Salvetti complexes for conditional oriented matroids
Combinatorics
2025-07-10 v1
Abstract
We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated oriented matroid. Our proof involves no choices, is relatively easy to visualize, and generalizes to the setting of conditional oriented matroids.
Cite
@article{arxiv.2507.06365,
title = {Salvetti complexes for conditional oriented matroids},
author = {Galen Dorpalen-Barry and Dan Dugger and Nicholas Proudfoot},
journal= {arXiv preprint arXiv:2507.06365},
year = {2025}
}