Groups, Geometry, and Dynamics


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Volume 9, Issue 1, 2015, pp. 275–316
DOI: 10.4171/GGD/313

Published online: 2015-04-28

Right-angled Artin groups and Out($\mathbb F_n$) – I. Quasi-isometric embeddings

Samuel J. Taylor[1]

(1) University of Texas at Austin, USA

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are modeled on the homomorphisms into the mapping class group constructed by Clay, Leininger, and Mangahas. Toward this goal, we develop tools in the free group setting that mirror those for surface groups and discuss various analogs of subsurface projection.

Keywords: Free group, outer automorphism group, Out($\mathbb F_n$), right-angled Artin group

Taylor Samuel: Right-angled Artin groups and Out($\mathbb F_n$) – I. Quasi-isometric embeddings. Groups Geom. Dyn. 9 (2015), 275-316. doi: 10.4171/GGD/313