Homological aperiodic tilings of 3-dimensional geometries

Abstract

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.

Withdrawn by the authors

References in corpus (2)

• Pattern equivariant functions and cohomology
• Topology of (some) tiling spaces without finite local complexity

Cited by in corpus (1)

• Aperiodic tilings of manifolds of intermediate growth