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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A twist over a minimal étale groupoid that is topologically nontrivial over the interior of the isotropy
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by Becky Armstrong, Abraham C. S. Ng, Aidan Sims and Yumiao Zhou;
Proc. Amer. Math. Soc. 153 (2025), 1849-1866
DOI: https://doi.org/10.1090/proc/17159
Published electronically: February 27, 2025

Abstract:

We present an example of a twist over a minimal Hausdorff étale groupoid such that the restriction of the twist to the interior of the isotropy is not topologically trivial; that is, the restricted twist is not induced by a continuous $2$-cocycle.
References
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Bibliographic Information
  • Becky Armstrong
  • Affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6012, New Zealand
  • MR Author ID: 1278315
  • ORCID: 0000-0002-2432-7003
  • Email: becky.armstrong@vuw.ac.nz
  • Abraham C. S. Ng
  • Affiliation: School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
  • MR Author ID: 1341810
  • ORCID: 0000-0002-1701-7904
  • Email: abraham.ng@sydney.edu.au
  • Aidan Sims
  • Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, New South Wales 2522, Australia
  • MR Author ID: 671497
  • ORCID: 0000-0002-1965-6451
  • Email: asims@uow.edu.au
  • Yumiao Zhou
  • Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, New South Wales 2522, Australia
  • ORCID: 0009-0008-7652-5328
  • Email: ymchou1989@outlook.com
  • Received by editor(s): May 19, 2024
  • Received by editor(s) in revised form: September 5, 2024
  • Published electronically: February 27, 2025
  • Additional Notes: This research was funded by a University of Wollongong AEGiS Connect Grant; the Australian Research Council grants DP180100595 and DP200100155; the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC 2044 – 390685587, Mathematics Münster – Dynamics – Geometry – Structure; the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 427320536 – SFB 1442; the ERC Advanced Grant 834267 – AMAREC; and the Marsden Fund of the Royal Society of New Zealand (grant number 21-VUW-156)
  • Communicated by: Matthew Kennedy
  • © Copyright 2025 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 153 (2025), 1849-1866
  • MSC (2020): Primary 18B40; Secondary 22A22
  • DOI: https://doi.org/10.1090/proc/17159
  • MathSciNet review: 4881379