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The topology of
arrangements of ideal type
Nils Amend and Gerhard Röhrle |
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Algebraic & Geometric Topology 19 (2019) 1341–1358
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Abstract |
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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 –arrangement. We study the –property for a certain class of subarrangements of Weyl arrangements, the so-called arrangements of ideal type . These stem from ideals in the set of positive roots of a reduced root system. We show that the –property holds for all arrangements if the underlying Weyl group is classical and that it extends to most of the if the underlying Weyl group is of exceptional type. Conjecturally this holds for all . In general, the are neither simplicial nor is their complexification of fiber type. |
Keywords
Weyl arrangement, arrangement of ideal type, $K(\pi,1)$
arrangement
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Mathematical Subject Classification 2010
Primary: 14N20, 20F55, 52C35
Secondary: 13N15
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References |
Publication
Received: 30 January 2018
Revised: 21 August 2018
Accepted: 24 October 2018
Published: 21 May 2019
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Authors |
| Nils Amend | |
| Institut für
Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Gottfried Wilhelm Leibniz Universität Hannover Hannover Germany |
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| Gerhard Röhrle | |
| Fakultät für Mathematik Ruhr-Universität Bochum Bochum Germany |
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