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

Abstract

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 corollary is that a pure braid group contains a closed hyperbolic manifold group as a quasi-isometrically embedded subgroup up to dimension eight. Finally, we show that the isomorphism problem, conjugacy problem, and membership problems are unsolvable in the class of finitely presented subgroups of braid groups.

The condition p>2 is included for the result on symplectomorphisms of the sphere. To appear in Geometry and Topology

Cited by in corpus (17)

• Quasi-isometric classification of right-angled Artin groups I: the finite out case
• Free products and the algebraic structure of diffeomorphism groups
• The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$
• Path lifting properties and embedding between RAAGs
• Diffeomorphism groups of critical regularity
• Special cubulation of strict hyperbolization
• Two-generator subgroups of right-angled Artin groups are quasi-isometrically embedded
• Embeddability of right-angled Artin groups on complements of trees
• Quasi-isometry invariants of weakly special square complexes
• On the complexity of finite subgraphs of the curve graph
• Right-angled Artin groups on finite subgraphs of disk graphs
• A short proof that the $L^p$-diameter of $Dif{f}_0(S,area)$ is infinite
• Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups
• Right-angled Artin groups and curve graphs of nonorientable surfaces
• The RAAGs on the complement graphs of path graphs in mapping class groups
• The model theory of the curve graph
• Actions of right-angled Artin groups in low dimensions