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  JP Journal of Geometry and Topology  
 ISSN: 0972-415X
 
 
 

     JP Journal of Geometry and Topology
    Volume 7, Issue 2, Pages 283 - 307 (July 2007)


ON CYCLIC FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH SYMMETRY

Yusheng Wang (P. R. China)

Received November 27, 2006; Revised April 6, 2007

References:



[1] G. Bredon, Introduction to Compact Transformation Groups, Vol. 48, Academic Press, 1972.

[2] K. S. Brown, Cohomology of Groups, Springer-Verlag, New York, 1982.

[3] J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, New York, 1975.

[4] F. Fang, S. Mendonca and X. Rong, A connectedness principle in the geometry of positive curvature, Comm. Anal. Geom. 13(2) (2005), 479-501.

[5] F. Fang and X. Rong, Homeomorphic classification of positively curved manifolds with almost maximal symmetry rank, Math. Ann. 332(1) (2005), 81-101.

[6] P. Frank, The fundamental groups of positively curved manifolds with symmetry, Thesis, 2005.

[7] P. Frank, X. Rong and Y. Wang, Fundamental groups of positively curved manifolds with symmetry, Preprint.

[8] M. Freedman, Topology of Four Manifolds, J. Differential Geom. 28 (1982), 357-453.

[9] K. Grove and C. Searle, Positively curved manifolds with maximal symmetry rank, J. Pure Appl. Algebra 91 (1994), 137-142.

[10] R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306.

[11] X. Rong, Positively curved manifolds with almost maximal symmetry rank, Geom. Dedicata 59 (2002), 157-182.

[12] X. Rong, Fundamental group of positively curved manifolds with local torus actions, Asian J. Math. 9(4) (2005), 545-560.

[13] X. Rong and Y. Wang, Fundamental group of manifolds with positive curvature and torus actions, Geom. Dedicata 113 (2005), 165-184.

[14] X. Rong and Y. Wang, A classification of fundamental groups of positively curved manifolds with symmetry, Preprint.

[15] K. Shankar, On the fundamental group of positively curved manifolds, J. Differential Geom. 51 (1999), 179-182.

[16] S. Smale, Generalized Poincaré conjecture in dimension Ann. Math.74 (1961), 391-466.

[17] K. Sugahara, The isometry group of and the diameter of a Riemannian manifold with positive curvature, Math. Japan 27 (1982), 631-634.

[18] B. Wilking, Torus actions on manifolds of positive sectional curvature, Acta Math. 191 (2003), 259-297.

[19] J. A. Wolf, The Spaces of Constant Curvature, McGraw-Hill Series in Higher Mathematics, 1976.

[20] S. T. Yau, Problem Section, Seminar on Differential Geometry, Vol. 102, Ann. Math. Stud., Princeton University Press, 1982, pp. 669-706.

Keywords and phrases: cyclic fundamental groups, positive sectional curvature, group actions.

Communicated by Yasuo Matsushita

 


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