Groups and Dynamics Seminar

Under what circumstances can a tiling space be an (unbranced) covering space of another? It's well known that Thue-Morse is the double cover of period doubling, but what does a double cover of Thue Morse of Fibonacci or Penrose look like? In this talkd, I'll show how to construct all of the (finite, regular) covers of the Fibonacci tiling and then generalize to covers of arbitrary (FLC, repetitive) tilings in arbitrary dimensions. Hopefully this construction will contemplent Jianlong Liu's talk last week, providing lost of examples to flesh out the abstract theorems that Jianlong proved. (Joint work with Franz G\" ahler and Jianlong Liu.)