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2019 The topology of arrangements of ideal type
Nils Amend, Gerhard Röhrle
Algebr. Geom. Topol. 19(3): 1341-1358 (2019). DOI: 10.2140/agt.2019.19.1341

Abstract

In 1962, Fadell and Neuwirth showed that the configuration space of the braid arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn conjectured this for all finite Coxeter groups. This in turn follows from Deligne’s seminal work from 1972, where he showed that the complexification of every real simplicial arrangement is a K ( π , 1 ) –arrangement.

We study the K ( π , 1 ) –property for a certain class of subarrangements of Weyl arrangements, the so-called arrangements of ideal type A . These stem from ideals  in the set of positive roots of a reduced root system. We show that the K ( π , 1 ) –property holds for all arrangements A if the underlying Weyl group is classical and that it extends to most of the A if the underlying Weyl group is of exceptional type. Conjecturally this holds for all A . In general, the A are neither simplicial nor is their complexification of fiber type.

Citation

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Nils Amend. Gerhard Röhrle. "The topology of arrangements of ideal type." Algebr. Geom. Topol. 19 (3) 1341 - 1358, 2019. https://doi.org/10.2140/agt.2019.19.1341

Information

Received: 30 January 2018; Revised: 21 August 2018; Accepted: 24 October 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07078606
MathSciNet: MR3954284
Digital Object Identifier: 10.2140/agt.2019.19.1341

Subjects:
Primary: 14N20, 20F55, 52C35
Secondary: 13N15

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2019
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