Topological dimension of the boundaries of some hyperbolic Out(Fn)graphs
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
hyperbolic groups
outer automorphism groups
dimension theory
mapping class groups
Gromov boundary
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
14589
A theorem of BestvinaBrombergFujiwara asserts that the mapping class group of a hyperbolic surface of finite type has finite asymptotic dimension; its proof relies on an earlier result of BellFujiwara stating that the curve complex has finite asymptotic dimension. The analogous statements are still open for Out(Fn). In joint work with Mladen Bestvina and Ric Wade, we give a first hint towards this, by obtaining a bound (linear in the rank n) on the topological dimension of the Gromov boundary of the graph of free factors of Fn (as well as some other hyperbolic Out(Fn)graphs).
Horbez Notes

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