Topological rigidity for hyperbolic manifolds

Authors:
F. T. Farrell and L. E. Jones

Journal:
Bull. Amer. Math. Soc. **19** (1988), 277-282

MSC (1985):
Primary 18F25, 22E40, 57D50

DOI:
https://doi.org/10.1090/S0273-0979-1988-15640-6

MathSciNet review:
940487

Full-text PDF Free Access

References | Similar Articles | Additional Information

- D. V. Anosov,
*Geodesic flows on closed Riemann manifolds with negative curvature.*, Proceedings of the Steklov Institute of Mathematics, No. 90 (1967), American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by S. Feder. MR**0242194** - D. Burghelea and R. Lashof,
*Stability of concordances and the suspension homomorphism*, Ann. of Math. (2)**105**(1977), no. 3, 449–472. MR**438365**, DOI https://doi.org/10.2307/1970919 - Steve Ferry,
*Homotoping $\varepsilon $-maps to homeomorphisms*, Amer. J. Math.**101**(1979), no. 3, 567–582. MR**533191**, DOI https://doi.org/10.2307/2373798 - F. T. Farrell and W. C. Hsiang,
*On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds*, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 325–337. MR**520509** - F. T. Farrell and W. C. Hsiang,
*On Novikov’s conjecture for nonpositively curved manifolds. I*, Ann. of Math. (2)**113**(1981), no. 1, 199–209. MR**604047**, DOI https://doi.org/10.2307/1971138 - F. T. Farrell and W. C. Hsiang,
*The stable topological-hyperbolic space form problem for complete manifolds of finite volume*, Invent. Math.**69**(1982), no. 1, 155–170. MR**671656**, DOI https://doi.org/10.1007/BF01389189 - F. T. Farrell and W. C. Hsiang,
*Topological characterization of flat and almost flat Riemannian manifolds $M^{n}$ $(n\not =3,\,4)$*, Amer. J. Math.**105**(1983), no. 3, 641–672. MR**704219**, DOI https://doi.org/10.2307/2374318 - F. T. Farrell and L. E. Jones,
*$K$-theory and dynamics. I*, Ann. of Math. (2)**124**(1986), no. 3, 531–569. MR**866708**, DOI https://doi.org/10.2307/2007092 - F. T. Farrell and L. E. Jones,
*$K$-theory and dynamics. II*, Ann. of Math. (2)**126**(1987), no. 3, 451–493. MR**916716**, DOI https://doi.org/10.2307/1971358 - F. T. Farrell and L. E. Jones,
*The surgery $L$-groups of poly-(finite or cyclic) groups*, Invent. Math.**91**(1988), no. 3, 559–586. MR**928498**, DOI https://doi.org/10.1007/BF01388787
11. F. T. Farrell and L. E. Jones, Foliated control theory. I and II, submitted for publication.
12. F. T. Farrell and L. E. Jones, Topological analogue of Mostow’s rigidity theorem, in preparation.
- M. Gromov,
*Manifolds of negative curvature*, J. Differential Geometry**13**(1978), no. 2, 223–230. MR**540941** - A. E. Hatcher,
*Concordance spaces, higher simple-homotopy theory, and applications*, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 3–21. MR**520490**
15. K. Igusa, Stability of pseudoisotopies, Seminar Notes 1, Aarhus Univ., Matematisk Institut, Aarhus, Denmark, 1982, pp. 27-37.
- Lowell Jones,
*The nonsimply connected characteristic variety theorem*, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 131–140. MR**520500** - Robion C. Kirby and Laurence C. Siebenmann,
*Foundational essays on topological manifolds, smoothings, and triangulations*, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1977. With notes by John Milnor and Michael Atiyah; Annals of Mathematics Studies, No. 88. MR**0645390** - G. D. Mostow,
*Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms*, Inst. Hautes Études Sci. Publ. Math.**34**(1968), 53–104. MR**236383** - Frank Quinn,
*Ends of maps. I*, Ann. of Math. (2)**110**(1979), no. 2, 275–331. MR**549490**, DOI https://doi.org/10.2307/1971262 - Friedhelm Waldhausen,
*Algebraic $K$-theory of topological spaces. I*, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 35–60. MR**520492** - C. T. C. Wall,
*Surgery on compact manifolds*, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. MR**0431216**
22. K. Igusa, The stability theorem for pseudoisotopies, preprint.

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