Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

A topological analogue of Mostow's rigidity theorem

Author(s): F. T. Farrell; L. E. Jones
Journal: J. Amer. Math. Soc. 2 (1989), 257-370.
MSC: Primary 57N15; Secondary 19B28, 22E40, 57R52, 57R67, 57S05, 58F17
MathSciNet review: 973309
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[1]
D. R. Anderson and W.-c. Hsiang, The functors $ {K_{ - i}}$ and pseudo-isotopies of polyhedra, Ann. of Math (2) 105 (1977), 201-223. MR 0440573 (55:13447)

[2]
D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., Vol. 90, Amer. Math. Soc., Providence, RI, 1969. MR 0242194 (39:3527)

[3]
W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Birkhäuser, Boston, 1985. MR 823981 (87h:53050)

[4]
R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. MR 0251664 (40:4891)

[5]
A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235-272. MR 0387496 (52:8338)

[6]
W. Browder and F. Quinn, A surgery theory for $ G$-manifolds and stratified sets, Manifolds--Tokyo 1973, Univ. of Tokyo Press, Tokyo, 1975, pp. 27-36. MR 0375348 (51:11543)

[7]
D. Burghelea and R. Lashof, The homotopy type of the space of diffeomorphisms. I, Trans. Amer. Math. Soc. 196 (1975), 1-36. MR 0356103 (50:8574)

[8]
-, The homotopy type of the space of diffeomorphisms. II, Trans. Amer. Math. Soc. 196 (1975), 37-50.

[9]
-, Stability of concordances and suspension homeomorphism, Ann. of Math. (2) 105 (1977), 449-472. MR 0438365 (55:11280)

[10]
D. Burghelea, Automorphisms of manifolds, Proc. Sympos. Pure Math., Vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 347-371. MR 520511 (80g:57001)

[11]
T. A. Chapman and S. Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979), 567-582. MR 533191 (81f:57007a)

[12]
D. Epstein and M. Shub, Expanding endomorphisms of flat manifolds, Topology 7 (1968), 139-141. MR 0227996 (37:3580)

[13]
F. T. Farrell, The obstruction to fibering a manifold over a circle, Indiana Univ. Math. J. 21 (1971), 315-346. MR 0290397 (44:7578)

[14]
F. T. Farrell and W.-c. Hsiang, Manifolds with $ {\pi _1} = G{ \times _\alpha }T$, Amer. J. Math. 95 (1973), 813-848. MR 0385867 (52:6726)

[15]
-, Rational $ L$-groups of Bieberbach groups, Comment. Math. Helv. 52 (1977), 89-109. MR 0448372 (56:6679)

[16]
-, The topological-Euclidean space form problem, Invent. Math. 45 (1978), 175-179. MR 0482771 (58:2824)

[17]
-, On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds, Proc. Sympos. Pure Math., Vol. 32, Amer. Math. Soc., Providence, RI, pp. 325-337. MR 520509 (80g:57043)

[18]
-, On Novikov's conjecture for non-positively curved manifolds, I, Ann. of Math. (2) 113 (1981), 199-209.

[19]
-, The Whitehead group of poly-(finite or cyclic) groups, J. London Math. Soc. (2) 24 (1981), 308-324. MR 631942 (83b:20041)

[20]
-, The stable topological-hyperbolic space form problem for finite volume manifolds, Invent. Math. 69 (1982), 155-170. MR 671656 (84c:57027)

[21]
-, Topological characterization of flat and almost flat Riemannian manifolds $ {M^n}\quad (n \ne 3,4)$, Amer. J. Math. 105 (1983), 641-672. MR 704219 (84k:57017)

[22]
F. T. Farrell and L. E. Jones, Algebraic $ K$-theory of spaces stratified fibred over hyperbolic orbifolds, Proc. Nat. Acad. Sci. U.S.A 83 (1986), 5364-5366. MR 851508 (87m:57039)

[23]
-, $ K$-theory and dynamics. I, Ann. of Math (2) 124 (1986), 531-569. MR 866708 (88f:57062)

[24]
-, Algebraic $ K$-theory of discrete subgroups of Lie groups, Proc. Nat. Acad. Sci. U.S.A. 84 (1987), 3095-3096. MR 887290 (88g:18011)

[25]
-, $ K$-theory and dynamics. II, Ann. of Math. (2) 126 (1987), 451-493. MR 916716 (89f:57029a)

[26]
-, The surgery $ L$-groups of poly-(finite or cyclic) groups, Invent. Math. 91 (1988), 559-586. MR 928498 (89d:57049)

[27]
-, Topological rigidity for hyperbolic manifolds, Bull. Amer. Math. Soc. 19 (1988), 277-282. MR 940487 (89f:57042)

[28]
-, Foliated control theory I, $ K$-theory 2 (1988), 357-399. MR 972605 (90e:57037)

[29]
-, Foliated control theory II, $ K$-theory 2 (1988), 401-430.

[30]
-, Splitting over flat and almost flat Riemannian manifolds (in preparation).

[31]
M. Freedman and F. Quinn, $ 4$-manifolds, Ann. of Math. Stud. (to appear).

[32]
M. Gromov, Manifolds of negative curvature, J. Differential Geom. 13 (1978), 223-230. MR 540941 (80h:53040)

[33]
A. E. Hatcher, Concordance spaces, higher simple homotopy theory, and applications, Proc. Sympos. Pure Math., Vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 3-21. MR 520490 (80f:57014)

[34]
A. Hatcher and J. Wagoner, Pseudo-isotopies of compact manifolds, Astérisque 6 (1973). MR 0353337 (50:5821)

[35]
N. J. Hicks, Notes on differential geometry, van Nostrand, Princeton, 1965. MR 0179691 (31:3936)

[36]
M. W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 0119214 (22:9980)

[37]
K. Igusa, The stability theorem for pseudoisotopies, $ K$-theory 2 (1988), 1-355. MR 972368 (90d:57035)

[38]
L. E. Jones, Patch spaces, Ann. of Math. (2) 97 (1973), 306-343. MR 0315720 (47:4269)

[39]
-, The non-simply connected characteristic variety theorem, Proc. Sympos. Pure Math., Vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 131-140.

[40]
-, Construction of surgery problems, Geometric Topology (J. Cantrell, ed.), Academic Press, NY, 1979, pp. 367-391. MR 537742 (80i:57023)

[41]
G. G. Kasparov, Topological invariants of elliptic operators. I. $ K$-homology, Izv. Akad. Nauk SSSR Ser Mat. 39 (1975), 796-838. MR 0488027 (58:7603)

[42]
-, Equivariant $ KK$-theory and the Novikov conjecture, Invent. Math. 91 (1988), 147-201. MR 918241 (88j:58123)

[43]
R. C. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, smoothings and triangulations, Ann. of Math. Stud., Vol. 88, Princeton Univ. Press, Princeton, NJ, 1977. MR 0645390 (58:31082)

[44]
H. Kneser, Geschlossene Flächen in dreidimensionalen Mannigfalligkeiten, Jahresber. Deutsch. Math.-Verein. 38 (1929), 248-260.

[45]
N. Levitt, Poincaré duality cobordism, Ann. of Math. (2) 96 (1972), 211-244. MR 0314059 (47:2611)

[46]
S. Maumary, Proper surgery groups and Wall-Novikov groups, Algebraic $ K$-theory. III, Lecture Notes in Math., Vol. 343, Springer, Berlin, 1973, pp. 526-539. MR 0377938 (51:14107)

[47]
J. Milnor, A unique factorization theorem for $ 3$-manifolds, Amer. J. Math. 84 (1962), 1-7. MR 0142125 (25:5518)

[48]
-, On fundamental groups of complete affinely flat manifolds, Adv. in Math. 25 (1977), 178-187. MR 0454886 (56:13130)

[49]
A. S. Mishchenko, Infinite dimensional representations of discrete groups and higher signatures, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 81-106. MR 0362407 (50:14848)

[50]
G. D. Mostow, Quasi-conformal mappings in $ n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1967), 53-104. MR 0236383 (38:4679)

[51]
-, Strong rigidity of locally symmetric spaces, Ann. of Math. Stud., Vol. 78, Princeton Univ. Press, Princeton, NJ, 1973. MR 0385004 (52:5874)

[52]
A. J. Nicas, Induction theorems for groups of homotopy manifold structures, Mem. Amer. Math. Soc., no. 267, 1982. MR 668807 (83i:57026)

[53]
-, An infinite family of non-Haken hyperbolic three-manifolds with vanishing Whitehead groups, Math. Proc. Cambridge Philos. Soc. 99 (1986), 239-246. MR 817665 (87h:57018)

[54]
A. J. Nicas and C. W. Stark, Whitehead groups of certain hyperbolic manifolds, Math. Proc. Cambridge Philos. Soc. 95 (1984), 299-308. MR 735370 (85k:18018b)

[55]
-, Whitehead groups of certain hyperbolic manifolds II, Combinatorial Group Theory and Topology, Ann. of Math. Studies, Vol. 111, Princeton Univ. Press, Princeton, NJ, 1987, pp. 415-432. MR 895625 (89a:57017)

[56]
G. Prasad, Strong rigidity of $ Q$-rank 1 lattices, Invent. Math. 21 (1973), 255-286. MR 0385005 (52:5875)

[57]
F. Quinn, A geometric formulation of surgery, Ph.D. thesis, Princeton University, 1969. MR 0282375 (43:8087)

[58]
-, A geometric formulation of surgery, Topology of Manifolds, Markham, Chicago, 1970, pp. 500-511. MR 0282375 (43:8087)

[59]
-, Ends of maps I, Ann. of Math. 110 (1979), 275-331. MR 549490 (82k:57009)

[60]
A. Ranicki, Algebraic $ L$-theory II: Laurent extensions, Proc. London Math. Soc. (3) 27 (1973), 126-158. MR 0414662 (54:2760b)

[61]
L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension $ > 5$, Ph.D. thesis, Princeton Univ., 1965.

[62]
L. Taylor, Surgery on paracompact manifolds, Ph.D. thesis, Univ. of California at Berkeley, 1972.

[63]
F. Waldhausen, Algebraic $ K$-theory of topological spaces I, Proc. Sympos. Pure Math., Vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 35-60. MR 520492 (81i:18014a)

[64]
C. T. C. Wall, Surgery on compact manifolds, Academic Press, London, 1971. MR 0431216 (55:4217)

[65]
F. Quinn, Ends of maps II, Invent. Math. 68 (1982), 353-424. MR 669423 (84j:57011)

[66]
F. T. Farrell and L. E. Jones, Compact negatively curved manifolds (of $ {\text{dim}} \ne 3,4$) are topologically rigid, Proc. Nat. Acad. Sci. U.S.A. (to appear). MR 997635 (90h:57023b)

[67]
-, Negatively curved manifolds with exotic smooth structures (submitted for publication).

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 57N15, 19B28, 22E40, 57R52, 57R67, 57S05, 58F17

Retrieve articles in all Journals with MSC: 57N15, 19B28, 22E40, 57R52, 57R67, 57S05, 58F17

Additional Information:

DOI: 10.1090/S0894-0347-1989-0973309-4
PII: S0894-0347-1989-0973309-4
Copyright of article: Copyright 1989, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia