Arrangements associated to chordal graphs and limits of colored braid groups
Frederic Chapoton, Patrick Polo
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 = GT 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(GT) is a limit over T of colored braid groups.
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