3 problems

GHW decomposition conjecture. There exists such a decomposition $(\ast)$ in which $\Gamma_1$ and $\Gamma_2$ are GHW Bieberbach groups of dimension $n-1$.

Multiplicity-free holonomy conjecture. For every finite group $H$, there exists a Bieberbach group $\Gamma$ with $\mathbb{Q}$-multiplicity-free holonomy representation…

An $n$-dimensional Bieberbach group is a torsion-free crystallographic group acting discretely and cocompactly on $\mathbb{R}^n$ by Euclidean isometries. Its holonomy group is the…