Camille Horbez (Orsay) - Abstract commensurator of some normal subgroups of Out(Fn)
Опубликовано: 29 Июль 2026
на канале: 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions
на канале: 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions
290
2
Graphs, surfaces, and cube complexes
12 July 2018
Abstract: We give a new proof of a theorem of Farb and Handel stating that for all n\ge 4, Out(Fn) is equal to its own abstract commensurator. In other words, every isomorphism between finite-index subgroups of Out(Fn) is the restriction of the conjugation by some element of Out(Fn). Our proof enables us to extend their theorem to the n=3 case. More generally, we prove that many normal subgroups of Out(Fn), for example the Torelli subgroup IA_n and all subgroups in the Johnson filtration of Out(Fn), have Out(Fn) as their abstract commensurator.
This is a joint work with Martin Bridson and Ric Wade.