Analogies between groups and subshifts : Higman type theorems for subshifts

Subshifts are sets of colorings of Z² by a finite alphabet that avoid some family of forbidden patterns. We investigate here some analogies with group theory that were first noticed by Emmanuel Jeandel. In particular we will show theorems on subshifts inspired by Higman’s embedding theorems of group theory, among which, the fact that subshifts with a computable language can be obtained as restrictions of minimal subshifts of finite type.

This is joint work with Emmanuel Jeandel.