Braid groups and right angled Artin groups

Frank Connolly; Margaret Doig

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Braid groups and right angled Artin groups

Frank Connolly·Margaret Doig

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Abstract

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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Frank Connolly, Margaret Doig. 2004-11-16. Braid groups and right angled Artin groups. https://arxiv.org/abs/math/0411368

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