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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Complete shrinking Ricci solitons have finite fundamental group
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by William Wylie PDF
Proc. Amer. Math. Soc. 136 (2008), 1803-1806 Request permission

Abstract:

We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of García-Río and Fernández-López in the compact case.
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Additional Information
  • William Wylie
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
  • Email: wylie@math.ucla.edu
  • Received by editor(s): March 29, 2007
  • Published electronically: October 18, 2007
  • Communicated by: Jon G. Wolfson
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 1803-1806
  • MSC (2000): Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-07-09174-5
  • MathSciNet review: 2373611