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arXiv · 1201.0919

Homological aperiodic tilings of 3-dimensional geometries

Piotr W. Nowak·Shmuel Weinberger
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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.

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BibTeXRIS

Piotr W. Nowak, Shmuel Weinberger. 2012-05-16. Homological aperiodic tilings of 3-dimensional geometries. https://arxiv.org/abs/1201.0919

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