Homological aperiodic tilings of 3-dimensional geometries
Group Theory
2012-05-17 v2 Dynamical Systems
Geometric Topology
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1201.0919,
title = {Homological aperiodic tilings of 3-dimensional geometries},
author = {Piotr W. Nowak and Shmuel Weinberger},
journal= {arXiv preprint arXiv:1201.0919},
year = {2012}
}
Comments
Withdrawn by the authors