Quasi-isometrically embedded subgroups of braid and diffeomorphism groups

John Crisp, Bert Wiest
2007 Transactions of the American Mathematical Society  
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(D 2 , ∂D 2 , vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L 2 -norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of F n and Z n for all n > 0. As a consequence we are also able to embed a variety of Gromov
more » ... erbolic groups quasi-isometrically in pure braid groups and in the group Diff(D 2 , ∂D 2 , 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.
doi:10.1090/s0002-9947-07-04332-2 fatcat:wfytxzvc2rfldmtp26d6ub6vui