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arXiv · 2507.06365

Salvetti complexes for conditional oriented matroids

Galen Dorpalen-Barry·Dan Dugger·Nicholas Proudfoot
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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.

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Galen Dorpalen-Barry, Dan Dugger, Nicholas Proudfoot. 2025-07-08. Salvetti complexes for conditional oriented matroids. https://arxiv.org/abs/2507.06365

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