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The Deligne complex for the four-strand braid group


Author: Ruth Charney
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3881-3897
MSC (2000): Primary 20F36, 20F55, 52C35
DOI: https://doi.org/10.1090/S0002-9947-03-03425-1
Published electronically: December 15, 2003
MathSciNet review: 2058510
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Abstract: This paper concerns the homotopy type of hyperplane arrangements associated to infinite Coxeter groups acting as reflection groups on $\mathbb C^n$. A long-standing conjecture states that the complement of such an arrangement should be aspherical. Some partial results on this conjecture were previously obtained by the author and M. Davis. In this paper, we extend those results to another class of Coxeter groups. The key technical result is that the spherical Deligne complex for the 4-strand braid group is CAT(1).


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Additional Information

Ruth Charney
Affiliation: Department of Mathematics, The Ohio State University, 231 W. 18th Ave, Columbus, Ohio 43210
Address at time of publication: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254
Email: charney@math.ohio-state.edu, charney@brandeis.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03425-1
Keywords: Artin groups, hyperplane arrangements
Received by editor(s): August 6, 2002
Received by editor(s) in revised form: May 1, 2003
Published electronically: December 15, 2003
Additional Notes: This work was partially supported by NSF grant DMS-0104026
Article copyright: © Copyright 2003 American Mathematical Society

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