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