Geometry & Topology

Anti-trees and right-angled Artin subgroups of braid groups

Sang-hyun Kim and Thomas Koberda

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Abstract

We prove that an arbitrary right-angled Artin group G 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 G is a quasi-isometrically embedded subgroup of the area-preserving diffeomorphism groups of the 2–disk and of the 2–sphere with Lp–metrics for suitable p. 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.

Article information

Source
Geom. Topol., Volume 19, Number 6 (2015), 3289-3306.

Dates
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
https://projecteuclid.org/euclid.gt/1510858875

Digital Object Identifier
doi:10.2140/gt.2015.19.3289

Mathematical Reviews number (MathSciNet)
MR3447104

Zentralblatt MATH identifier
1351.20021

Subjects
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

Keywords
right-angled Artin group braid group cancellation theory hyperbolic manifold quasi-isometry

Citation

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


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