5 problems

Let $X\subset\mathbb R^3$ be a Delone set with parameter $R$. For each point $x\in X$, let $S_x(2R)$ be its local group, and let $K$ be the subset of points whose local groups cont…

Let $N$ be a connected and simply connected nilpotent Lie group, and let $\Gamma\subseteq\operatorname{Aff}(N)$ act properly discontinuously and cocompactly on $N$; such an action…

Let $G$ be a finite cyclic group and $L$ a finitely generated $\mathbb{Z}G$-lattice. For the split crystallographic group $L\rtimes G$, consider its integral cohomology and the coh…

Let $\Gamma<\operatorname{Isom}(\mathbb{R}^k)$ be a torsion-free crystallographic group. Its quotient $\mathbb{R}^k/\Gamma$ is a closed aspherical manifold, and…

Let $G$ be a finite cyclic group and let $L$ be a finitely generated $\mathbb ZG$-lattice. For the semidirect product extension … consider its Lyndon–Hochschild–Serre spectral sequ…