Geometry & Topology
- Geom. Topol.
- Volume 19, Number 6 (2015), 3289-3306.
Anti-trees and right-angled Artin subgroups of braid groups
We prove that an arbitrary right-angled Artin group admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree, and, consequently, into a pure braid group. It follows that is a quasi-isometrically embedded subgroup of the area-preserving diffeomorphism groups of the –disk and of the –sphere with –metrics for suitable . Another corollary is that there exists a closed hyperbolic manifold group of each dimension which admits a quasi-isometric group embedding into a pure braid group. Finally, we show that the isomorphism problem, conjugacy problem, and membership problem are unsolvable in the class of finitely presented subgroups of braid groups.
Geom. Topol., Volume 19, Number 6 (2015), 3289-3306.
Received: 27 May 2014
Revised: 2 February 2015
Accepted: 6 April 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F36: Braid groups; Artin groups
Secondary: 53D05: Symplectic manifolds, general 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20F67: Hyperbolic groups and nonpositively curved groups
Kim, Sang-hyun; Koberda, Thomas. Anti-trees and right-angled Artin subgroups of braid groups. Geom. Topol. 19 (2015), no. 6, 3289--3306. doi:10.2140/gt.2015.19.3289. https://projecteuclid.org/euclid.gt/1510858875