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.
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© 2017, Springer Science+Business Media New York.
- Bratteli–Vershik system
- Groupoid of germs
- Inverse semigroup
- Smale space
- Tight groupoid