The asphericity conjecture for arrangements of ideal type

Let Φ\Phi be a reduced root system with Weyl arrangement A(Φ)\mathscr A(\Phi). An arrangement of ideal type AI\mathscr A_{\mathcal I} is a subarrangement of A(Φ)\mathscr A(\Phi) determined by an ideal I\mathcal I in the positive roots of Φ\Phi. Asphericity conjecture. Any subarrangement of ideal type AI\mathscr A_{\mathcal I} of A(Φ)\mathscr A(\Phi) is a K(π,1)K(\pi,1)-arrangement. The preceding results prove the claim for all classical root systems and for many arrangements in exceptional types, leaving only the listed exceptional cases unresolved.

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Primary source

Nils Amend and Gerhard Roehrle, “The topology of arrangements of ideal type”, arXiv:1801.07157 (2018).

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