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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-9,
author = {Zhenlei Zhang},
title = {On the finiteness of the fundamental group of a compact shrinking Ricci soliton},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {297-299},
zbl = {1116.53027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-9}
}
Zhenlei Zhang. On the finiteness of the fundamental group of a compact shrinking Ricci soliton. Colloquium Mathematicae, Tome 107 (2007) pp. 297-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-9/