# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Directional expansiveness of Penrose tilings"

#### Jang, Hyeeun

We extend a well known theorem Keynes-Robertson (1969) that a homeomorphism of a compact metric space is a factor of a subshift to $\mathbb{Z}^d$ version, which is used for tensor product (product type) action and tiling flows. This development forms a new theorem that tensor product action of two subshifts has just vertical and horizontal non-expansive directions. On this basis, our main result of the thesis shows that the Penrose tiling dynamical system has exactly five non-strongly expansive directions. The proof involves using Wang tiles to show that Penrose tilings are essentially tensor products of two Sturmian dynamical systems.

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