On the fundamental group of a compact negatively curved manifold

Chen, Su Shing

doi:10.1090/S0002-9939-1978-0514740-5

On the fundamental group of a compact negatively curved manifold

Author: Su Shing Chen
Journal: Proc. Amer. Math. Soc. 71 (1978), 119-122
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1978-0514740-5
MathSciNet review: 0514740
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A question of Hirsch and Thurston on the fundamental group of a compact negatively curved manifold is investigated.

[1] W. Byers, On a theorem of Preissmann, Proc. Amer. Math. Soc. 24 (1970), 50-51. MR 0251665 (40:4892)
[2] S. Chen, Complete homogeneous Riemannian manifolds of negative sectional curvature, Comment. Math. Helv. 50 (1975), 115-122. MR 0372783 (51:8989)
[3] -, A remark on a question of Margulis, Duke Math. J. 43 (1976), 805-808. MR 0507232 (58:22392)
[4] P. Eberlein, Some properties of the fundamental group of a fuchsian manifold, Invent. Math. 19 (1973), 5-13. MR 0400250 (53:4085)
[5] P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-109. MR 0336648 (49:1421)
[6] P. E. Ehrlich, The Dirichlet fundamental region and elliptic isometries for Riemannian manifolds without conjugate points (preprint).
[7] D. Gromoll and J. A. Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77 (1971), 545-552. MR 0281122 (43:6841)
[8] M. W. Hirsch and W. P. Thurston, Foliated bundles, invariant measures and flat manifolds, Ann. of Math. 101 (1975), 369-390. MR 0370615 (51:6842)
[9] J. Lehner, Discontinuous groups and automorphic functions, Math. Surveys, no. 8, Amer. Math. Soc., Providence, R.I., 1964. MR 0164033 (29:1332)
[10] T. S. Motzkin, B. O'Neill and E. G. Straus, Isolated subgroups, Michigan Math. J. 20 (1973), 235-248. MR 0318329 (47:6876)
[11] A. Preissmann, Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv. 15 (1942-43), 175-216. MR 0010459 (6:20g)
[12] S. T. Yau, On the fundamental group of compact manifolds of nonpositive curvature, Ann. of Math. 93 (1971), 579-585. MR 0283726 (44:956)
[13] J. Stallings, Group theory and three-dimensional manifolds, Yale Math. Monographs No. 4, Yale University, New Haven, Conn., 1971. MR 0415622 (54:3705)
[14] R. G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 588-610. MR 0240177 (39:1531)