1 6 N ov 2 00 4 Braid Groups and Right Angled Artin Groups Frank Connolly and Margaret Doig

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...

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

On the Cohomology Rings of Tree Braid Groups

Let Γ be a graph. The (unlabelled) configuration space UCnΓ of n points on Γ is the space of n-element subsets of Γ. The n-strand braid group of Γ, denoted BnΓ, is the fundamental group of UCnΓ. We use the methods and results of [10] to get a partial description of the cohomology rings H∗(BnT ), where T is a tree. Our results are then used to prove that BnT is a right-angled Artin group if and ...

Presentations of subgroups of the braid group generated by powers of band generators

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements σi are presented by the commutators of generators which are powers of commuting elements. Hence they are naturally presented as right-angled Artin groups. The case of subgroups generated by powers of the band generators aij is more involved. We show...

Anti-trees and right-angled Artin subgroups of braid groups

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...