An Obstruction to Fundamental Groups of Positively Ricci Curved Manifolds

Author： Wu J-Y.  

Publisher： Springer Publishing Company

ISSN： 0232-704X

Source： Annals of Global Analysis and Geometry, Vol.16, Iss.4, 1998-08, pp. : 371-382

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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.

Related content

Positively Curved Manifolds with Almost Maximal Symmetry Rank

By Rong X.  

Geometriae Dedicata, Vol. 95, Iss. 1, 2002-12 ,pp. : 157-182 (26)

Springer Publishing Company

Access to resources Recommend Favorite

Growth of Certain Non-positively Curved Cube Groups

By Noskov G.A.  

European Journal of Combinatorics, Vol. 21, Iss. 5, 2000-07 ,pp. : 659-666 (8)

Elsevier

Access to resources Recommend Favorite

On the growth of fundamental groups of nonpositive curvature manifolds

By  

Bulletin of the Australian Mathematical Society, Vol. 54, Iss. 3, 1996-12 ,pp. : 483-487 (5)

Cambridge University Press

Access to resources Recommend Favorite

Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

By Zhou Xiang   Liu Wei  

Acta Mathematica Sinica, Vol. 20, Iss. 4, 2004-07 ,pp. : 605-612 (8)

Springer Publishing Company

Access to resources Recommend Favorite

Fundamental Groups of Closed Manifolds with Positive Curvature and Torus Actions

By Rong Xiaochun   Wang Yusheng  

Geometriae Dedicata, Vol. 113, Iss. 1, 2005-06 ,pp. : 165-184 (20)

Springer Publishing Company

Access to resources Recommend Favorite