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WIELER SOLENOIDS : NON-HAUSDORFF EXPANSIVENESS, CUNTZ-PIMSNER MODELS, AND FUNCTORIAL PROPERTIES

Deeley, Robin J. ; Eryüzlü, Menevşe ; Goffeng, Magnus LU orcid and Yashinski, Allan (2025) In Transactions of the American Mathematical Society 378(10). p.7033-7074
Abstract

Building on work of Williams,Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this result, the first and fourth listed authors of the present paper showed that the stable C∗-algebra associated to such a Smale space can be obtained from a stationary inductive limit of a Fell algebra. Its spectrum is typically non-Hausdorff and admits a self-map related to the stationary inverse limit. With the goal of understanding the fine structure of the stable algebra and the stable Ruelle algebra, we study said self-map on the spectrum of the Fell algebra as a dynamical system in its own right. Our results can be summarized into the statement that this... (More)

Building on work of Williams,Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this result, the first and fourth listed authors of the present paper showed that the stable C∗-algebra associated to such a Smale space can be obtained from a stationary inductive limit of a Fell algebra. Its spectrum is typically non-Hausdorff and admits a self-map related to the stationary inverse limit. With the goal of understanding the fine structure of the stable algebra and the stable Ruelle algebra, we study said self-map on the spectrum of the Fell algebra as a dynamical system in its own right. Our results can be summarized into the statement that this dynamical system is an expansive, surjective, local homeomorphism of a compact, locally Hausdorff space and from its K-theory we can compute K-theoretical invariants of the stable and unstable Ruelle algebra of a Smale space with totally disconnected stable sets.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Transactions of the American Mathematical Society
volume
378
issue
10
pages
42 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:105018395993
ISSN
0002-9947
DOI
10.1090/tran/9478
language
English
LU publication?
yes
id
2ce10b4a-7b46-403e-9b05-5f0170f37a3b
date added to LUP
2026-01-08 15:30:12
date last changed
2026-01-08 15:30:59
@article{2ce10b4a-7b46-403e-9b05-5f0170f37a3b,
  abstract     = {{<p>Building on work of Williams,Wieler proved that every irreducible Smale space with totally disconnected stable sets can be realized via a stationary inverse limit. Using this result, the first and fourth listed authors of the present paper showed that the stable C∗-algebra associated to such a Smale space can be obtained from a stationary inductive limit of a Fell algebra. Its spectrum is typically non-Hausdorff and admits a self-map related to the stationary inverse limit. With the goal of understanding the fine structure of the stable algebra and the stable Ruelle algebra, we study said self-map on the spectrum of the Fell algebra as a dynamical system in its own right. Our results can be summarized into the statement that this dynamical system is an expansive, surjective, local homeomorphism of a compact, locally Hausdorff space and from its K-theory we can compute K-theoretical invariants of the stable and unstable Ruelle algebra of a Smale space with totally disconnected stable sets.</p>}},
  author       = {{Deeley, Robin J. and Eryüzlü, Menevşe and Goffeng, Magnus and Yashinski, Allan}},
  issn         = {{0002-9947}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{7033--7074}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Transactions of the American Mathematical Society}},
  title        = {{WIELER SOLENOIDS : NON-HAUSDORFF EXPANSIVENESS, CUNTZ-PIMSNER MODELS, AND FUNCTORIAL PROPERTIES}},
  url          = {{http://dx.doi.org/10.1090/tran/9478}},
  doi          = {{10.1090/tran/9478}},
  volume       = {{378}},
  year         = {{2025}},
}