Inverse semigroups associated with one-dimensional generalized solenoids

Abstract

In this paper, we study inverse semigroups defined on the Bratteli–Vershik systems and SFT covers of 1-solenoids. We show that groupoids of germs of these inverse semigroups are equivalent to the unstable equivalence groupoids of 1-solenoids. Then we prove that Exel’s tight C∗-algebras of inverse semigroups are strongly Morita equivalent to the unstable C∗-algebras of 1-solenoids. © 2017, Springer Science+Business Media New York.