Homological aperiodic tilings of 3-dimensional geometries

Details Homological aperiodic tilings of 3-dimensional geometries Homological aperiodic tilings of 3-dimensional geometries

2012-01-04

arxiv.org/abs/1201.0919v1

Mathematics

Group Theory

7 figures

Scientific paper

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.

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