5 problems

Let $\mathcal{M}$ be the class of maps under consideration, let $\operatorname{invlim} f$ denote the inverse limit of $f$, let $\chi_f$ be the substitution associated with $f$, and…

A Pisot substitution in one dimension is a substitution whose substitution matrix has one eigenvalue strictly greater than $1$ and all other eigenvalues strictly between $0$ and…

Let $\sigma$ be an irreducible Pisot substitution, and let the associated substitution dynamical system and its strong coincidence condition be understood. Strong coincidence conje…

Global gap-labeling conjecture. The weak-coupling restriction, namely the existence of $\delta>0$ requiring $0<\left\Vert(\mathfrak{p},\mathfrak{q})-(1,0)\right\Vert<\delta$, can b…

Let a one-dimensional substitution tiling space have dilatation a degree $d$ Pisot number, and suppose that its first rational Čech cohomology has dimension $d$. For these homologi…