4 problems

Bellissard's gap-labelling conjecture.

Let $\Sigma$ be a Cantor set with a minimal action of $\mathbb{Z}^p$ that preserves a Borel probability measure $\mu$. Let $\sigma$ be the multiplier on $\mathbb{Z}^p$ associated t…

Magnetic gap-labelling conjecture for strongly minimal actions. If the action is strongly minimal, then the containment in the magnetic gap-labelling conjecture for minimal actions…

Magnetic gap-labelling conjecture. The magnetic gap-labelling group is contained in the subgroup of $\mathbb R$ given by