6533b871fe1ef96bd12d11e3
RESEARCH PRODUCT
Quasi-isometrically embedded subgroups of braid and diffeomorphism groups
John CrispBert Wiestsubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Fundamental group[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Hyperbolic groupGeneral MathematicsBraid group20F36braid groupGroup Theory (math.GR)01 natural sciencesRelatively hyperbolic group[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]right-angled Artin groupCombinatoricssymbols.namesakeMathematics - Geometric TopologyMathematics::Group Theory05C25hyperbolic group[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesBraidFOS: Mathematics0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsGeometric Topology (math.GT)Braid theoryMathematics::Geometric TopologyPlanar graphsymbols010307 mathematical physicsDiffeomorphismMathematics - Group Theory20F36; 05C25description
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 $L^2$-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 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-06-19 |