The asphericity conjecture for arrangements of ideal type

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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.

References

Primary source

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

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