Inverse semigroups associated with one-dimensional generalized solenoids

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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.

Original languageEnglish
Pages (from-to)81-104
Number of pages24
JournalSemigroup Forum
Issue number1
StatePublished - 1 Feb 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.


  • 1-Solenoid
  • Bratteli–Vershik system
  • Groupoid of germs
  • Inverse semigroup
  • Smale space
  • Tight groupoid


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