Most graph braid groups are not classical braid groups

Details Most graph braid groups are not classical braid groups Most graph braid groups are not classical braid groups

2010-10-29

arxiv.org/abs/1010.6286v3

Mathematics

Group Theory

17 pages, 2 figures

Scientific paper

We will prove that the first Betti number of most graph braid groups is strictly greater than 1 and thus not isomorphic to any classical braid group. Additionally, we will explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. We will then use this to construct an embedding of a graph braid group into a classical pure braid group. Finally we will describe all homomorphisms from the classical braid group on at least 4 strands into right-angled Artin groups, and that the image is isomorphic to $\mathbb{Z}$.

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