Bulletin (New Series) of the American Mathematical Society

Rigidity and other topological aspects of compact nonpositively curved manifolds

F. T. Farrell and L. E. Jones

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 22, Number 1 (1990), 59-64.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183555454

Mathematical Reviews number (MathSciNet)
MR1001606

Zentralblatt MATH identifier
0703.57018

Subjects
Primary: 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 57D50

Citation

Farrell, F. T.; Jones, L. E. Rigidity and other topological aspects of compact nonpositively curved manifolds. Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 1, 59--64. https://projecteuclid.org/euclid.bams/1183555454


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References

  • 1. W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of non-positive curvature, Birkhäuser, Boston, 1985.
  • 2. H. Bass, A. Heller, and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 61-79.
  • 3. D. Burghelea and R. Lashof, Stability of concordances and the suspension homomorphism, Ann. of Math. (2) 105 (1977), 449-472.
  • 4. F. T. Farrell and W.-C. Hsiang, The Whitehead group of poly- (finite or cyclic) groups, J. London Math. Soc. 24 (1981), 308-324.
  • 5. F. T. Farrell and W.-C. Hsiang, On Novikov's conjecture for nonpositively curved manifolds. I, Ann. of Math. (2) 113 (1981), 199-209.
  • 6. F. T. Farrell and W.-C. Hsiang, Topological characterizations of flat and almost flat Riemannian manifolds Mn (n ≠ 3, 4), Amer. J. Math. 105 (1983), 641-672.
  • 7. F. T. Farrell and L. E. Jones, K-theory and dynamics. I, Ann. of Math. (2) 124 (1986), 531-569.
  • 8. F. T. Farrell and L. E. Jones, K-theory and dynamics. II, Ann. of Math. (2) 126 (1987), 451-493.
  • 9. F. T. Farrell and L. E. Jones, A topological analogue of Mostow's rigidity theorem, J. Amer. Math. Soc. 2 (1989), 257-370.
  • 10. F. T. Farrell and L. E. Jones, Compact negatively curved manifolds (of dim ≠ 3, 4) are topological rigid, Proc. Nat. Acad. Sci. 86 (1989), 3461-3463.
  • 11. F. T. Farrell and L. E. Jones, Negatively curved manifolds with exotic smooth structures, J. Amer. Math. Soc. 2 (1989), 899-908.
  • 12. F. T. Farrell and L. E. Jones, Foliated control without radius of injectivity restrictions, Topology (in press).
  • 13. F. T. Farrell and L. E. Jones, Foliated control theory. I and II, K-theory 2 (1988), 357-399 and 401-430.
  • 14. F. T. Farrell and L. E. Jones, Algebraic K-theory of discrete subgroups of Lie groups, Proc. Nat. Acad. Sci. 84 (1987), 3095-3096.
  • 15. F. T. Farrell and L. E. Jones, The surgery L-groups of poly-(finite or cyclic) groups, Invent. Math. 91 (1988), 559-586.
  • 16. D. Gromoll and J. Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of non-positive curvature, Bull. Amer. Math. Soc. 77 (1971), 545-552.
  • 17. A. Hatcher, Concordance spaces, higher simple homotopy theory, and applications, Proc. Sympos. Pure Math. 32 (1978), 3-21.
  • 18. B. Hu, Ph. D. Thesis, SUNY at Stony Brook, 1989.
  • 19. K. Igusa, The stability theorem for smooth pseudo-isotopies, K -Theory 2 (1988), 1-355.
  • 20. R. C. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Ann. of Math. Studies 88, Princeton Univ. Press, Princeton, N.J., 1977.
  • 21. A. J. Nicas, On the higher Whitehead groups of a Bieberbach group, Trans. Amer. Math. Soc. 287 (1985), 853-859.
  • 22. F. Quinn, Ends of maps. I, Ann. of Math. (2) 110 (1979), 275-331.
  • 23. F. Quinn, Ends of maps. II, Invent. Math. 68 (1982), 353-424.
  • 24. F. Quinn, Algebraic K-theory of poly-(finite or cyclic) groups, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 221-226.
  • 25. F. Waldhausen, Algebraic K-theory of topological spaces I, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R.I., 1978, pp. 35-60.
  • 26. C. T. C. Wall, Surgery on compact manifolds, Academic Press, New York, 1970.
  • 27. S.-T. Yau, Seminar on differential geometry, Annals. of Math. Studies, Princeton Univ. Press, Princeton, N.J., 1982.
  • 28. S.-T. Yau, On the fundamental group of compact manifolds of non-positive curvature, Ann. of Math. (2) 93 (1971), 579-585.