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Topological dimension of the boundaries of some hyperbolic Out(Fn)-graphs

Introductory Workshop: Geometric Group Theory August 22, 2016 - August 26, 2016

August 22, 2016 (02:30 PM PDT - 03:20 PM PDT)
Speaker(s): Camille Horbez (Université de Paris XI)
Location: MSRI: Simons Auditorium
  • geometric group theory

  • hyperbolic groups

  • outer automorphism groups

  • dimension theory

  • mapping class groups

  • Gromov boundary

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



A theorem of Bestvina-Bromberg-Fujiwara 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 Bell-Fujiwara 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).

26638?type=thumb Horbez Notes 198 KB application/pdf Download
Video/Audio Files


H.264 Video 14589.mp4 308 MB video/mp4 rtsp://videos.msri.org/data/000/026/446/original/14589.mp4 Download
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