Constructing Menger manifold C*-diagonals in classifiable C*-algebras

Li, X. (2022) Constructing Menger manifold C*-diagonals in classifiable C*-algebras. International Mathematics Research Notices, 2022(23), pp. 18992-19053. (doi: 10.1093/imrn/rnab199)

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We initiate a detailed analysis of C*-diagonals in classifiable C*-algebras, answering natural questions concerning topological properties of their spectra and uniqueness questions. Firstly, we construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras, which are unital or stably projectionless with continuous scale. Secondly, for classifiable stably finite C*-algebras with torsion-free K0 and trivial K1⁠, we further determine the spectra of the C*-diagonals up to homeomorphism. In the unital case, the underlying space turns out to be the Menger curve. In the stably projectionless case, the space is obtained by removing a non-locally-separating copy of the Cantor space from the Menger curve. Thirdly, we show that each of our classifiable C*-algebras has continuum many pairwise non-conjugate such Menger manifold C*-diagonals.

Item Type:Articles
Additional Information:This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817597).
Glasgow Author(s) Enlighten ID:Li, Professor Xin
Authors: Li, X.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
Publisher:Oxford University Press
ISSN (Online):1687-0247
Published Online:08 September 2021
Copyright Holders:Copyright © 2021 The Author
First Published:First published in International Mathematics Research Notices 2022(23): 18992-19053
Publisher Policy:Reproduced under a Creative Commons licence

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