2025/07/08 by Galen Dorpalen‐Barry, Dorpalen-Barry, Galen, Dan Dugger +3
Computer Science · Mathematics · #52B40 #52C35 #52C40 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2507.06365
openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.