#### Vol. 308, No. 1, 2020

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On the topological dimension of the Gromov boundaries of some hyperbolic ${\mathrm{Out}}(F_N)$-graphs

### Mladen Bestvina, Camille Horbez and Richard D. Wade

Vol. 308 (2020), No. 1, 1–40
##### Abstract

We give upper bounds, linear in the rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.

##### Keywords
free factor graph, free factor complex, boundary, topological dimension, automorphism, free group
##### Mathematical Subject Classification 2010
Primary: 20F28, 20F65
##### Milestones
Received: 12 February 2019
Revised: 20 December 2019
Accepted: 7 May 2020
Published: 3 December 2020
##### Authors
 Mladen Bestvina Department of Mathematics University of Utah Salt Lake City, UT United States Camille Horbez Laboratoire de Mathématiques d’Orsay Université Paris Sud, CNRS Université Paris-Saclay Orsay France Richard D. Wade Mathematical Institute University of Oxford Oxford United Kingdom