Salvetti complexes for conditional oriented matroids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913933181321216 |
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| author | Dorpalen-Barry, Galen Dugger, Dan Proudfoot, Nicholas |
| author_facet | Dorpalen-Barry, Galen Dugger, Dan Proudfoot, Nicholas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Salvetti complexes for conditional oriented matroids Dorpalen-Barry, Galen Dugger, Dan Proudfoot, Nicholas Combinatorics 52C35, 52C40, 52B40 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. |
| title | Salvetti complexes for conditional oriented matroids |
| topic | Combinatorics 52C35, 52C40, 52B40 |
| url | https://arxiv.org/abs/2507.06365 |