%0 Journal Article
%T Homological aperiodic tilings of 3-dimensional geometries
%A Piotr W. Nowak
%A Shmuel Weinberger
%J Mathematics
%D 2012
%I arXiv
%X We construct the first aperiodic tiles for two amenable 3-dimensional Lie groups: Sol and the Heisenberg group. Our construction relies on the use of higher-dimensional uniformly finite homology. In particular, we settle completely the existence of aperiodic tiles for all of the non-compact geometries of 3-manifolds appearing in the geometrization conjecture.
%U http://arxiv.org/abs/1201.0919v2