Circle Maps and C*-algebras

Thomas Lundsgaard Schmidt, Klaus Thomsen

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We consider a construction of $C^*$-algebras from
continuous piecewise monotone maps on the circle which generalizes
the crossed product construction for homeomorphisms and more
generally the construction of Renault, Deaconu and
Anantharaman-Delaroche for local homeomorphisms. Assuming that the
map is surjective and not locally injective we give necessary and sufficient
conditions for the simplicity of the $C^*$-algebra and show that it
is then a Kirchberg algebra. We provide tools for the
calculation of the K-theory groups and turn them into an
algorithmic method for Markov maps.
Translated title of the contributionCirkelafbildninger og C*-algebraer
Original languageEnglish
JournalErgodic Theory and Dynamical Systems
Pages (from-to)546-584
Number of pages39
Publication statusPublished - 2015

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