The Deligne complex for the four-strand braid group-Reference-Cited by-同舟云学术

The Deligne complex for the four-strand braid group

Published:2003-12-15 Issue:10 Volume:356 Page:3881-3897
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Charney Ruth

Abstract

This paper concerns the homotopy type of hyperplane arrangements associated to infinite Coxeter groups acting as reflection groups on C n \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).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2004-356-10/S0002-9947-03-03425-1/S0002-9947-03-03425-1.pdf

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2. Injectivity of the positive monoid for some infinite type Artin groups;Charney, Ruth,1999

3. The Tits conjecture for locally reducible Artin groups;Charney, Ruth;Internat. J. Algebra Comput.,2000

4. Finite 𝐾(𝜋,1)s for Artin groups;Charney, Ruth,1995

5. The 𝐾(𝜋,1)-problem for hyperplane complements associated to infinite reflection groups;Charney, Ruth;J. Amer. Math. Soc.,1995

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