An Obstruction to Fundamental Groups of Positively Ricci Curved Manifolds

Author: Wu J-Y.¹

Source: Annals of Global Analysis and Geometry, Volume 16, Number 4, August 1998 , pp. 371-382(12)

Publisher: Springer

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Abstract:

In this note we propose a conjecture concerning fundamental groups of Riemannian n-manifolds with positive Ricci curvature. We prove a partial result under an extra condition on a lower bound of sectional curvature. Our main tool is the theory of Hausdorff convergence. We also extend Fukaya and Yamaguchi's resolution of a conjecture of Gromov to limit spaces which may have singular points.

Keywords: fundamental group; Hausdorff convergence; positive Ricci curvature

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Mathematics, National Chung Cheng University, Chia-Yi 621, Taiwan, R.O.C. (E-mail: jywu@math.ccu.edu.tw)

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