Quasi-isometrically embedded subgroups of braid and diffeomorphism groups
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- by John Crisp and Bert Wiest PDF
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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 $\operatorname {Diff}(D^2,\partial D^2,\operatorname {vol})$ 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 $\mathbb Z^n$ 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 group $\operatorname {Diff}(D^2,\partial D^2,\operatorname {vol})$. Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3-manifold.References
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Additional Information
- John Crisp
- Affiliation: Institut de Mathémathiques de Bourgogne (IMB), UMR 5584 du CNRS, Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078 Dijon cedex, France
- Email: jcrisp@u-bourgogne.fr
- Bert Wiest
- Affiliation: IRMAR, UMR 6625 du CNRS, Campus de Beaulieu, Université de Rennes 1, 35042 Rennes, France
- MR Author ID: 631096
- Email: bertold.wiest@univ-rennes1.fr
- Received by editor(s): July 6, 2005
- Received by editor(s) in revised form: October 4, 2005
- Published electronically: June 22, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 5485-5503
- MSC (2000): Primary 20F36, 05C25
- DOI: https://doi.org/10.1090/S0002-9947-07-04332-2
- MathSciNet review: 2327038