Tiling Problems on Baumslag-Solitar groups
@inproceedings{Aubrun2013TilingPO, title={Tiling Problems on Baumslag-Solitar groups}, author={Nathalie Aubrun and Jarkko Kari}, booktitle={MCU}, year={2013} }
We exhibit a weakly aperiodic tile set for Baumslag-Solitar groups, and prove that the domino problem is undecidable on these groups. A consequence of our construction is the existence of an arecursive tile set on Baumslag-Solitar groups.
33 Citations
Addendum to "Tilings problems on Baumslag-Solitar groups"
- MathematicsArXiv
- 2021
This addendum clarified the point that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for BS(m,n) given in the paper, and gave a detailed proof of the undecidability result.
Aperiodic Subshifts on Polycyclic Groups
- MathematicsArXiv
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We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].
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It is shown that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property and applied to the fundamental group of any closed orientable surface of genus at least 2.
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- 2016
The domino problem for tilings over self-similar structures of \(\mathbb {Z}^d\) given by forbidden patterns is defined and non-trivial families of subsets with decidable and undecidable Domino problem are exhibited.
Aperiodic subshifts of finite type on groups which are not finitely generated
- Mathematics
- 2022
We provide an example of a non-finitely generated group which admits a nonempty strongly aperiodic SFT. Furthermore, we completely characterize the groups with this property in terms of their finitely…
The domino problem on groups of polynomial growth
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We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson.…
Some Notes about Subshifts on Groups
- MathematicsArXiv
- 2015
If a finitely presented group G admits a strongly aperiodic SFT, then G has decidable word problem, and this is true for the free group with 2 generators, Thompson's groups T and V, PSL2(Z) and any f.g. group of rational matrices which is bounded.
Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups
- MathematicsArXiv
- 2020
It is shown that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs, and that there exists a strongly a periodicity SFT on BS(n,n), which is similar to that presented by Aubrun and Kari.
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