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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Some topological results of Ricci limit spaces
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by Jiayin Pan and Jikang Wang PDF
Trans. Amer. Math. Soc. 375 (2022), 8445-8464 Request permission

Abstract:

We study the topology of a Ricci limit space $(X,p)$, which is the Gromov-Hausdorff limit of a sequence of complete $n$-manifolds $(M_i, p_i)$ with $\mathrm {Ric}\ge -(n-1)$. Our first result shows that, if $M_i$ has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is non-collapsed, then $X$ is semi-locally simply connected. In the process, we establish a slice theorem for isometric pseudo-group actions on a closed ball in the Ricci limit space. In the second result, we give a description of the universal cover of $X$ if $M_i$ has a uniform diameter bound; this improves a result by Ennis and Wei [Differential Geom. Appl. 24 (2006), pp. 554-562].
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Additional Information
  • Jiayin Pan
  • Affiliation: Department of Mathematics, University of California, Santa Cruz, California
  • MR Author ID: 1356847
  • Email: jpan53@ucsc.edu
  • Jikang Wang
  • Affiliation: Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada
  • ORCID: 0000-0001-9085-0217
  • Email: jikangwang1117@gmail.com
  • Received by editor(s): April 12, 2021
  • Received by editor(s) in revised form: August 4, 2021
  • Published electronically: October 3, 2022
  • Additional Notes: The first author was supported by the Fields Institute for Research in Mathematical Sciences.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8445-8464
  • MSC (2020): Primary 53C20
  • DOI: https://doi.org/10.1090/tran/8549