Braid groups and right angled Artin groups

The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that this braid group is a right angled Artin group if X is planar. We prove their conjecture if X is a tree whose nodes all lie in a single interval of X.

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Keywords

Mathematics - Geometric Topology, 57S30(primary), 57Q05(secondary), 20F36, FOS: Mathematics, Geometric Topology (math.GT), Group Theory (math.GR), Mathematics - Group Theory

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