Arrangements associated to chordal graphs and limits of colored braid groups

2003/03/24 by Frederic Chapoton, Frédéric Chapoton, Chapoton, Frederic +2
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.AT #msc:05C38 #msc:18A30 #msc:20F36 #msc:52C35 #msc:55R10

paper · pdf · doi:10.48550/arxiv.math/0303283

11 pages

arxiv created 2003/03/24 · arxiv updated 2009/11/30

Abstract

Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Gamma(G) the fundamental group of X(G). We show that Gamma(G) is a limit of colored braid groups over the poset of simplices of G. When G = G_T is the comparability graph associated with a rooted tree T, a case recently investigated by the first author, the result takes the following very simple form: Gamma(G_T) is a limit over T of colored braid groups.

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