Non-vanishing of homotopy groups of Manin--Schechtman arrangements
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913127494320128 |
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| author | Saito, Takuya Yamagata, So |
| author_facet | Saito, Takuya Yamagata, So |
| contents | One of the central problems in the topology of hyperplane arrangements is determining whether the complement is a $K(π,1)$-space. In this paper, we study Manin--Schechtman arrangements, introduced as higher-dimensional analogs of the braid arrangement, and prove that their complements have non-vanishing higher homotopy groups. Consequently, these arrangements fail to be $K(π,1)$ in a broad range of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-vanishing of homotopy groups of Manin--Schechtman arrangements Saito, Takuya Yamagata, So Algebraic Topology Algebraic Geometry Combinatorics 55P20, 52C35, 14N20 One of the central problems in the topology of hyperplane arrangements is determining whether the complement is a $K(π,1)$-space. In this paper, we study Manin--Schechtman arrangements, introduced as higher-dimensional analogs of the braid arrangement, and prove that their complements have non-vanishing higher homotopy groups. Consequently, these arrangements fail to be $K(π,1)$ in a broad range of cases. |
| title | Non-vanishing of homotopy groups of Manin--Schechtman arrangements |
| topic | Algebraic Topology Algebraic Geometry Combinatorics 55P20, 52C35, 14N20 |
| url | https://arxiv.org/abs/2605.14536 |