Geodesic
Homomorphisms between multidimensional constant-shape substitutions
Christopher Cabezas1
1Université de Picardie Jules Verne, Amiens, France; University of Liège, Belgium
Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1259-1323

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DOI

We study a class of Zd-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of Zd. We prove that any measurable factor map and even any homomorphism associated to a matrix commuting with the expansion matrix, induces a continuous one. We also get strong restrictions on the normalizer group, proving that any endomorphism is invertible, the normalizer group is virtually generated by the shift action and the quotient of the normalizer group by the automorphisms is restricted by the digit tile of the substitution.
DOI : 10.4171/ggd/726
Classification : 37-XX, 52-XX
Mots-clés : Homomorphisms, automorphism groups, substitutive subshifts, digit tiles, nondeterministic directions

Christopher Cabezas  1

1 Université de Picardie Jules Verne, Amiens, France; University of Liège, Belgium 
Christopher Cabezas. Homomorphisms between multidimensional constant-shape substitutions. Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1259-1323. doi: 10.4171/ggd/726
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     year = {2023},
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     doi = {10.4171/ggd/726},
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