Embedding right-angled Artin groups into graph braid groups

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Embedding Right-angled Artin Groups into Graph Braid Groups

We construct an embedding of any right-angled Artin group into a graph braid group. We include an observation which decreases the number of strands of the graph braid group required for this embedding, yielding an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.

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Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to rightangled Artin groups a result of Lyndon for free gr...

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We prove that an arbitrary right-angled Artin group G admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, G admits quasi-isometric group embeddings into a pure braid group and into the area-preserving diffeomorphism groups of the 2–disk and the 2–sphere, answering questions due to Crisp–Wiest and M. Kapovich. Another co...

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Surface Subgroups of Right-Angled Artin Groups

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ژورنال

عنوان ژورنال: Geometriae Dedicata

سال: 2006

ISSN: 0046-5755,1572-9168

DOI: 10.1007/s10711-006-9101-0