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HOMOLOGY AND MATUI’S HK CONJECTURE FOR GROUPOIDS ON ONE-DIMENSIONAL SOLENOIDS

Part of: Topological dynamics Selfadjoint operator algebras Topological and differentiable algebraic systems

Published online by Cambridge University Press:  17 May 2019

INHYEOP YI Open the ORCID record for INHYEOP YI [Opens in a new window]
INHYEOP YI*
Affiliation:
Department of Mathematics Education, Ewha Womans University, Seoul, Korea email [email protected]
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Abstract

We show that Matui’s HK conjecture holds for groupoids of unstable equivalence relations and their corresponding $C^{\ast }$-algebras on one-dimensional solenoids.

Keywords

one-dimensional solenoidSmale spacestable Ruelle algebragroupoidhomology groupsHK conjecture

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 22A22: Topological groupoids (including differentiable and Lie groupoids) 46L05: General theory of $C^*$-algebras 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 105 - 117
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048313).

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