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math.GR2012★ 7 cited
Aperiodic tilings of manifolds of intermediate growth
Michał Marcinkowski, Piotr W. Nowak
We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.
math.GR2012★ 1 cited
Homological aperiodic tilings of 3-dimensional geometries
Piotr W. Nowak, Shmuel Weinberger
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 f…