Jon Aaronson (TAU) On the bounded cohomology of actions of multidimensional groups.

Although each cocycle for a action of the integers is specified by the sequence of Birkhoff sums of a function, it is relatively difficult to specify cocycles for the actions of multidimensional groups such as $\Bbb Z^2$. We'll see that if $(X,T)$ is a transitive action of the finitely generated (countable) group $\Gamma$ by homeomorphism of the polish space $X$, and $\Bbb B$ is a separable Banach space, there is a cocycle $F:\Gamma\times X \to\Bbb B$ with each $x\mapsto F(g,x)$ bounded and continuous so that the skew product action $(X x \Bbb B,S)$ is transitive where $S_g(x,b)=(T_gx,b+F(g,x))$. Depending on time available, we'll also discuss measure theoretic analogues. This result was shown for transitive actions of the integers by E.A. Sidorov in 1973. Joint work with Benjamin Weiss: arXiv:1712.05196

Date: 

Tue, 06/11/2018 - 14:15 to 15:15