36th Summer Topology Conference

July 18-22, 2022

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

"Substitution tilings with transcendental inflation factor"

Frettlöh, Dirk

Tiling spaces are topological spaces whose elements are aperiodic biinfinite words (consisting of letters) or aperiodic tilings (consisting of tiles, hence in 1D: intervals of different lengths). Usually there are only finitely many types of letters, respectively tiles. Quite often the words or tilings are constructed via a substituion rule (i.e., inflate, subdivide). In this case the inflation factor is always an algebraic number. Only recently tilings with infinitely many tile types were studied in more detail w.r.t. their topological and dynamical properties. The question arose whether there are substitution rules with transcendental inflation factor (and then necessarily infinitely many letters resp. tile types). This talk explains concepts and background and gives an affirmative answer. This is joint work with Alexey Garber (UT Rio Grande Valley) and Neil Mañibo (OU Milton Keynes)

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