Advanced Studies in Pure Mathematics

RAAGs in Diffeos

Sang-hyun Kim and Thomas Koberda

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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

Hyperbolic Geometry and Geometric Group Theory, K. Fujiwara, S. Kojima and K. Ohshika, eds. (Tokyo: Mathematical Society of Japan, 2017), 215-224

Received: 31 January 2015
Revised: 1 July 2015
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538671946

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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


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.

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