The codimension one homology of a complete manifold with nonnegative Ricci curvature

American Journal of Mathematics

Volumn 123, Issue 3, 2001, Pages 515-524

  Shen, Zhongmin ^a   Sormani, Christina ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035374214     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2001.0020     Document Type: Article

References (9)

1. J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971/72), 119-128.
2. Y. Itokawa and R. Kobayashi, Minimizing currents in open manifolds and the n-1 homology of nonnegatively Ricci curved manifolds, Amer. J. Math. 121 (1999), 1253-1278.
3. W. S. Massey, A Basic Course in Algebraic Topology. Graduate Texts in Math., vol. 127, Springer-Verlag, New York, 1991.
4. J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley Publishing Company, Menlo Park, CA, 1984.
5. Z. Shen, On complete manifolds of nonnegative kth-Ricci curvature, Trans. Amer. Math. Soc. 338 (1993), 289-310.
6. _, Complete manifolds with nonnegative Ricci curvature and large volume growth, Invent. Math. 125 (1996), 393-404.
7. C. Sormani, The rigidity and almost rigidity of manifolds with minimal volume growth, Comm. Anal. Geom. 8 (2000), 159-212.
8. _, On loops representing elements of the fundamental group of a complete manifold with nonnegative Ricci curvature, preprint, February, 1999.
9. S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659-670.