Periodicity of tilings of Baumslag-Solitar groups (webinaire)

LIP, ENS de Lyon

Date(s) : 09/06/2020
11 h 00 min - 12 h 00 min


Étienne Moutot (ENS Lyon)

Periodicity is a key property of tilings, and express the fact that a tiling may repeat itself.
When tiling a surface that is more complicated than a line (ℤ), there are different definitions of periodicity that are not equivalent. We will be interested in what is called weak and strong periodicity and aperiodicity.

In this presentation, we look at tilings of Baumslag-Solitar groups BS(m,n), and we show that for BS(1,n) and BS(n,n) (the residually finite case), there exists both weakly and strongly aperiodic tilesets.

Aubrun and Kari presented a weakly aperiodic tileset for BS(m,n) groups, and the starting point of our work was to remark that their tileset is in fact strongly aperiodic for BS(1,n). Then we were able to build a weakly aperiodic tileset for BS(1,n) based on substitutions on words, and a strongly aperiodic one for BS(n,n).

All of this is a joint work with Julien Esnay.


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