On the fundamental group of a compact negatively curved manifold

On the fundamental group of a compact negatively curved manifold
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Proc. Amer. Math. Soc. 71 (1978), 119-122 Request permission

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

References

William P. Byers, On a theorem of Preissmann, Proc. Amer. Math. Soc. 24 (1970), 50–51. MR 251665, DOI 10.1090/S0002-9939-1970-0251665-X
Su Shing Chen, Complete homogeneous Riemannian manifolds of negative sectional curvature, Comment. Math. Helv. 50 (1975), 115–122. MR 372783, DOI 10.1007/BF02565738
Su Shing Chen, A remark on a question of Margulis, Duke Math. J. 43 (1976), no. 4, 805–808. MR 507232
Patrick Eberlein, Some properties of the fundamental group of a Fuchsian manifold, Invent. Math. 19 (1973), 5–13. MR 400250, DOI 10.1007/BF01418848
P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. MR 336648

The Dirichlet fundamental region and elliptic isometries for Riemannian manifolds without conjugate points

Detlef Gromoll and Joseph 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 281122, DOI 10.1090/S0002-9904-1971-12747-7
Morris W. Hirsch and William P. Thurston, Foliated bundles, invariant measures and flat manifolds, Ann. of Math. (2) 101 (1975), 369–390. MR 370615, DOI 10.2307/1970996
Joseph Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, No. VIII, American Mathematical Society, Providence, R.I., 1964. MR 0164033
T. S. Motzkin, Barret O’Neill, and E. G. Straus, Isolated subgroups, Michigan Math. J. 20 (1973), 235–248. MR 318329
Alexandre Preissmann, Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv. 15 (1943), 175–216 (French). MR 10459, DOI 10.1007/BF02565638
Shing-tung Yau, On the fundamental group of compact manifolds of non-positive curvature, Ann. of Math. (2) 93 (1971), 579–585. MR 283726, DOI 10.2307/1970888
John Stallings, Group theory and three-dimensional manifolds, Yale Mathematical Monographs, vol. 4, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1969. MR 0415622
Richard G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585–610. MR 240177, DOI 10.1016/0021-8693(69)90030-1