Highly transitive actions of Out (Fn) Academic Article uri icon


  • 1.1. Highly transitive actions. The group Out(Fn) = Aut(Fn)/Inn(Fn) of outer automorphisms of the free group attracted much attention in the last couple of decades. The theory that is developed around this group runs parallel to that of the mapping class group of a surface Mod(Σg) = Out(π1(Σg)) and the special linear group SLn(Z) = Out(Zn). The questions that are asked about the first two groups are often motivated by the more classical theory of the arithmetic group SLn(Z) but sometimes the answers exhibit new and interesting phenomena. In the lowest non-trivial case these three families coincide Out(F2) = Mod(Σ1) = SL2(Z) and then they ramify in different directions. Moreover, for large values of n all three theories exhibit interesting “higher rank” phenomena that are not shared by the group SL2(Z). Due to the efforts of many mathematicians, notably Margulis, we can exhibit today an …

publication date

  • January 1, 2010