Event № 287
The Out(G)-action on the group cohomology H^n(G) of a group G is an important object of study in group theory. On the contrary, almost nothing is known about the corresponding Out(G)-action on the bounded group cohomology H^n_b(G). This talk will introduce bounded group cohomology and then look at the case of G=F_2 and n=2. There the dynamics of the unipotent elements in Out(F_2) on a dense subset C(F_2) of H^2_b(F_2) will be presented concretely and visualized. In particular we will show that no element of C(F_2) is fixed by the Out(F_2)-action, partly answering a question of Miklós Abért.