On the finiteness of the fundamental group of a compact shrinking Ricci soliton
Volume 107 / 2007
Colloquium Mathematicum 107 (2007), 297-299
MSC: Primary 53C25; Secondary 53C21, 55Q52.
DOI: 10.4064/cm107-2-9
Abstract
Myers's classical theorem says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Using Ambrose's compactness criterion or J. Lott's results, M. Fernández-López and E. García-Río showed that the finiteness of the fundamental group remains valid for a compact shrinking Ricci soliton. We give a self-contained proof of this fact by estimating the lengths of shortest geodesic loops in each homotopy class.
