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

Tue, 06/11/201814:15-15:15
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
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