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- W4297609097 abstract "Let $V$ be a finite dimensional complex vector space and $Wsubseteq GL(V)$ be a finite complex reflection group. Let $V^{reg}$ be the complement in $V$ of the reflecting hyperplanes. We prove that $V^{reg}$ is a $K(pi,1)$ space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection groups. The complexified real case follows from a theorem of Deligne and, after contributions by Nakamura and Orlik-Solomon, only six exceptional cases remained open. In addition to solving this six cases, our approach is applicable to most previously known cases, including complexified real groups for which we obtain a new proof, based on new geometric objects. We also address a number of questions about $pi_1(Wcq V^{reg})$, the braid group of $W$. This includes a description of periodic elements in terms of a braid analog of Springer's theory of regular elements." @default.
- W4297609097 created "2022-09-30" @default.
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- W4297609097 date "2006-10-26" @default.
- W4297609097 modified "2023-10-14" @default.
- W4297609097 title "Finite complex reflection arrangements are K(pi,1)" @default.
- W4297609097 doi "https://doi.org/10.48550/arxiv.math/0610777" @default.
- W4297609097 hasPublicationYear "2006" @default.
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