2 problems

Measurable cocycle quotient conjecture. For any measurable map $\omega\mapsto \rho_\omega$ from $\Omega$ to $Z^1_{<m}(G,X,S^1)$, there exists a set of positive measure…

Let $(X,T)$ be a topological dynamical system whose enveloping semigroup is a $d$-step topologically nilpotent group, with $d>2$. Iteratively define factors $X_j$ so that $X_j$ is…