## Advanced Studies in Pure Mathematics

### RAAGs in Diffeos

#### Abstract

We survey embeddability results related to RAAGs (right-angled Artin groups) and various automorphism groups of manifolds. We give two different methods of embedding a RAAG to into another, and deduce that every RAAG embeds into some braid groups. This gives the unsolvability of the isomorphism problem for finitely presented subgroups of braid groups. Also, we prove that every RAAG is a quasi-isometrically embedded subgroup of the symplectomorphism groups of the disk and the sphere, given with suitable $L^p$ metrics. Finally, we embed RAAGs in the smooth diffeomorphism group of the real line. These results reveal many closed hyperbolic manifold subgroups of diffeomorphism groups of manifolds.

#### Article information

Dates
Revised: 1 July 2015
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538671946

Digital Object Identifier
doi:10.2969/aspm/07310215

Mathematical Reviews number (MathSciNet)
MR3728499

#### Citation

Kim, Sang-hyun; Koberda, Thomas. RAAGs in Diffeos. Hyperbolic Geometry and Geometric Group Theory, 215--224, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07310215. https://projecteuclid.org/euclid.aspm/1538671946