Topological Self-joinings of Cartan Actions by Toral Automorphisms

Elon Lindenstrauss, Zhiren Wang

We show that if $r\ge 3$ and $\alpha$ is a faithful $Z^r$-Cartan action on a torus $T^d$ by automorphisms, then any closed subset of $(T^d{)}^2$ which is invariant and topologically tran…