6 problems

Kumjian–Pask–Sims conjecture. The cubical and categorical cohomology groups should be isomorphic in all dimensions:

Let a general higher-rank graph be given, and consider the inverse semigroup constructed from it as in Farthing, Muhly, and Yeend (2005). Let $G_\mathrm{tight}$ denote the tight gr…

q-independence conjecture. The $C^*$-algebra $C^*_0(G)$ should be isomorphic to $C^*_q(G)$ for every $q\in(0,1)$.

A higher-rank tree is a higher-rank graph arising from the construction associated with a polyhedral graph, and it is planar when the underlying graph is embedded in a sphere. Assu…

Let $C$ be a higher rank graph such that the associated Boolean inverse monoid is countably infinite, and suppose that $C$ also satisfies the condition of Proposition 4.9 of KP. Le…

Abundance conjecture. The Perron–Frobenius measure is potentially just one of many probability measures that could give faithful representations of the Cuntz–Krieger $C^*$-algebra…