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arXiv · 2605.14536

Non-vanishing of homotopy groups of Manin--Schechtman arrangements

Takuya Saito·So Yamagata
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Abstract

One of the central problems in the topology of hyperplane arrangements is determining whether the complement is a $K(\pi,1)$-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 $K(\pi,1)$ in a broad range of cases.

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Takuya Saito, So Yamagata. 2026-05-14. Non-vanishing of homotopy groups of Manin--Schechtman arrangements. https://arxiv.org/abs/2605.14536

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