Valérie Berthé: Dimension groups and recurrence for tree subshifts

Abstract: Dimension groups are invariants of orbital equivalence. We show in this lecture how to compute the dimension group of tree subshifts. Tree subshifts are defined in terms of extension graphs that describe the left and right extensions of factors of their languages: the extension graphs are trees. This class of subshifts includes classical families such as Sturmian, Arnoux-Rauzy subshifts, or else, codings of interval exchanges. We rely on return word properties for tree subshifts: every finite word in the language of a tree word admits exactly d return words, where d is the cardinality of the alphabet.
This is joint work with P. Cecchi, F. Dolce, F. Durand, J. Leroy, D. Perrin, S. Petite.

Recording during the Jean-Morlet chair research school "Tilings and Recurrence " the December 07, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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