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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Ricci flow and diffeomorphism groups of 3-manifolds
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by Richard H. Bamler and Bruce Kleiner
J. Amer. Math. Soc. 36 (2023), 563-589
Published electronically: August 12, 2022


We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai’s theorem for hyperbolic $3$-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms, except $S^3$ and $RP^3$, as well as hyperbolic manifolds, to prove that the space of metrics of constant sectional curvature is contractible. As a corollary, for such a $3$-manifold $X$, the inclusion $\operatorname {Isom}(X,g)\rightarrow \operatorname {Diff}(X)$ is a homotopy equivalence for any Riemannian metric $g$ of constant sectional curvature.
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Bibliographic Information
  • Richard H. Bamler
  • Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
  • MR Author ID: 976245
  • ORCID: 0000-0003-0872-9712
  • Email:
  • Bruce Kleiner
  • Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012
  • MR Author ID: 269190
  • Email:
  • Received by editor(s): January 4, 2018
  • Received by editor(s) in revised form: February 16, 2022
  • Published electronically: August 12, 2022
  • Additional Notes: The first author was supported by a Sloan Research Fellowship and NSF grant DMS-1611906. The second author was supported by NSF grants DMS-1405899, DMS-1406394, DMS-1711556, and a Simons Collaboration grant
  • © Copyright 2022 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 36 (2023), 563-589
  • MSC (2020): Primary 53E20, 57R50
  • DOI:
  • MathSciNet review: 4536904