On the domino problem of the Baumslag-Solitar groups

Kari Jarkko; Aubrun Nathalie
On the domino problem of the Baumslag-Solitar groups

Kari Jarkko
Aubrun Nathalie
Katso/Avaa
Lataukset: 

Elsevier B.V.
doi:10.1016/j.tcs.2021.09.002
URI
https://www.sciencedirect.com/science/article/pii/S030439752100517X
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Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021102752695
Tiivistelmä

In [1] we construct aperiodic tile sets on the Baumslag-Solitar groups BS(m, n). Aperiodicity plays a central role in the undecidability of the classical domino problem on Z2, and analogously to this we state as a corollary of the main construction that the Domino problem is undecidable on all Baumslag-Solitar groups. In the present work we elaborate on the claim and provide a full proof of this fact. We also provide details of another result reported in [1]: there are tiles that tile the Baumslag-Solitar group BS(m, n)but none of the valid tilings is recursive. The proofs are based on simulating piecewise affine functions by tiles on BS(m, n).

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