Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

A bound for the order of the fundamental group of a complete noncompact Ricci shrinker


Authors: Bennett Chow and Peng Lu
Journal: Proc. Amer. Math. Soc. 144 (2016), 2623-2625
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/proc/12983
Published electronically: December 15, 2015
MathSciNet review: 3477080
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the case of a complete noncompact shrinking gradient Ricci soliton, building upon the works of Derdzinski, Fernández-López and García-Rio, Lott, Naber, and Wylie, we obtain a bound for the order of its fundamental group $ \pi _1$ in terms of the dimension $ n$ and the logarithmic Sobolev constant. Under the additional assumption of being strongly $ \kappa $-noncollapsed, a bound for the order of $ \pi _1$ is $ \kappa ^{-1}$ times a function of $ n$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C44

Retrieve articles in all journals with MSC (2010): 53C44


Additional Information

Bennett Chow
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093

Peng Lu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

DOI: https://doi.org/10.1090/proc/12983
Received by editor(s): July 14, 2015
Published electronically: December 15, 2015
Additional Notes: The second author was partially supported by a grant from the Simons Foundation.
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society