Quasi-isometrically embedded subgroups of braid and diffeomorphism groups

2005/06/19 by John Crisp, Crisp, John, Bert Wiest +1
Mathematics · #05C25 #20F36 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:05C25 #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0506375

23 pages, 6 figures

arxiv created 2005/06/19 · arxiv updated 2016/09/07

Abstract

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 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 F_n 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 diffeomorphism group of the disk. Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3-manifold.

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