# '22

36th Summer Topology Conference

July 18-22, 2022

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

### "Homomorphisms between multidimensional substitutive subshifts."

#### Cabezas, Christopher

Homomorphisms are topological factors between topological dynamical systems, up to $GL(d,Z)$-transformations. This notion extends the classical dynamical ones like factor, conjugacies and automorphisms. While the automorphism group is the centralizer of the action group in the group of self-homeomorphisms in the phase space, the isomorphism group (invertible homomorphisms) is the normalizer of the action group. In this talk we will present some recent results about some rigidity properties of homomorphisms between substitutive subshifts generated by constant-shape substitutions. Constant-shape substitutions are a multidimensional generalization of constant-length substitutions, where any letter is assigned a pattern with the same shape.

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