Quasi-isometrically Embedded Subgroups of Braid and Diffeomorphism Groups
نویسندگان
چکیده
We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of Fn and Zn for all n > 0. As a consequence we are also able to embed a variety of Gromov hyperbolic groups quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol). Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3-manifold.
منابع مشابه
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...
متن کاملCyclic Subgroups are Quasi-isometrically Embedded in the Thompson-Stein Groups
We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson-Stein groups F (n1, ..., nk) such that n1 − 1|ni − 1 ∀i ∈ {1, ..., k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the ThompsonStein groups. This result al...
متن کاملGeometric quasi-isometric embeddings into Thompson's group F
We use geometric techniques to investigate several examples of quasi-isometrically embedded subgroups of Thompson’s group F . Many of these are explored using the metric properties of the shift map φ in F . These subgroups have simple geometric but complicated algebraic descriptions. We present them to illustrate the intricate geometry of Thompson’s group F as well as the interplay between its ...
متن کاملThe geometry of right angled Artin subgroups of mapping class groups
We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmüller space is a quasiisometric embedding for both of the standard metrics. As a consequence, we produce infinitely many genus h surfaces (for any h at least 2)...
متن کاملConvex Cocompactness in Mapping Class Groups via Quasiconvexity in Right-angled Artin Groups
We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H < G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconve...
متن کامل