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Isomorphism conjectures in algebraic $ K$-theory


Authors: F. T. Farrell and L. E. Jones
Journal: J. Amer. Math. Soc. 6 (1993), 249-297
MSC: Primary 57N37; Secondary 19D55
DOI: https://doi.org/10.1090/S0894-0347-1993-1179537-0
MathSciNet review: 1179537
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  • [1] R. Anderson and W.-c. Hsiang, The functors $ {K_{ - i}}$ and pseudoisotopies of polyhedra, Ann. of Math. (2) 105 (1977), 201-223. MR 0440573 (55:13447)
  • [2] W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Birkhäuser, Basel, 1985. MR 823981 (87h:53050)
  • [3] H. Bass, Algebraic $ K$-theory, W. A. Benjamin, New York, 1968. MR 0249491 (40:2736)
  • [3a] P. Baum and A. Connes, $ K$-theory for discrete groups, Operator Algebras and Applications, Cambridge Univ. Press, London and New York, 1988, pp. 1-20. MR 996437 (91i:46083)
  • [3b] -, Chern character for discrete groups, A Fete of Topology, Academic Press, San Diego, CA, 1988, pp. 163-232. MR 928402 (90e:58149)
  • [4] M. Bokstedt, W.-c. Hsiang, and I. Madsen, Cyclotomic trace and the $ K$-theoretic analogue of Novikov's conjecture, preprint.
  • [5] W. Browder, Manifolds with $ {\pi _1} = Z$, Bull Amer. Math. Soc. 72 (1966), 238-244. MR 0190940 (32:8350)
  • [6] D. Burghelea and R. Lashof, Stability of concordances and the suspension homomorphism, Ann. of Math. (2) 105 (1977), 449-472. MR 0438365 (55:11280)
  • [7] S. Cappell, Manifolds with fundamental group a generalized free product. I, Bull. Amer. Math. Soc. 80 (1974), 1193-1198. MR 0356091 (50:8562)
  • [8] D. Carter, Lower $ K$-theory of finite groups, Comm. Algebra 8 (1980), 1927-1937. MR 590500 (81m:16027)
  • [9] F. Connolly and T. Koz'niewski, Finiteness properties of classifying spaces of proper $ \Gamma $-actions, J. Pure Appl. Algebra, vol. 41, North-Holland, Amsterdam and New York, 1986, pp. 17-36. MR 844461 (87j:57026)
  • [10] G. F. Cooke and R. L. Finney, Homology of cell complexes, Math. Notes, vol. 4, Princeton Univ. Press, Princeton, NJ, 1967. MR 0219059 (36:2142)
  • [11] 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)
  • [12] -, The Whitehead groups of poly-(finite by cyclic) groups, J. London Math. Soc. (2) 24 (1982), 308-324.
  • [13] -, On Novikov's conjecture for cocompact discrete subgroups of a Lie group, Lecture Notes in Math., vol. 1051, Springer-Verlag, New York, 1984, pp. 38-48.
  • [14] -, Addendum to: On Novikov's conjecture for cocompact subgroups of a Lie group, Topology Appl. 26 (1987), 93-95. MR 893806 (88h:57030)
  • [15] F. T. Farrell and L. E. Jones, Foliated control theory. I, $ {\text{K}}$-theory 2 (1988), 357-399. MR 972605 (90e:57037)
  • [16] -, A topological analogue of Mostow's rigidity theorem, J. Amer. Math. Soc. 2 (1989), 257-370. MR 973309 (90h:57023a)
  • [17] -, The surgery $ L$-groups of poly-(finite or cyclic) groups, Invent. Math. 91 (1988), 559-586. MR 928498 (89d:57049)
  • [18] -, $ K$-theory and dynamics. I, II, Ann. of Math. (2) 124 (1986), 531-569; II, Ann. of Math. (2) 126 (1987), 451-493. MR 866708 (88f:57062)
  • [19] -, Algebraic $ K$-theory of spaces stratified fibered over hyperbolic orbifolds, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 5364-5366. MR 851508 (87m:57039)
  • [20] -, Algebraic $ K$-theory of discrete subgroups of Lie groups, Proc. Nat. Acad. Sci. U.S.A. 84 (1987), 3095-3096. MR 887290 (88g:18011)
  • [21] -, Rigidity and other topological aspects of non-positively curved manifolds, Bull. Amer. Math. Soc. 22 (1990), 59-64. MR 1001606 (90h:57023c)
  • [22] -, Computations of stable pseudoisotopy spaces for aspherical manifolds, Algebraic topology, Poznan 1989, Lecture Notes in Math., vol. 1474, Springer, Berlin, Heidelberg, and New York, 1991, pp. 59-74. MR 1133892 (92k:57038)
  • [23] -, Pseudoisotopy spaces of special affine manifolds, work in progress.
  • [24] -, Stable pseudoisotopy spaces of non-positively curved manifolds, J. Differential Geom. 34 (1991), 769-834. MR 1139646 (93b:57020)
  • [25] -, Topological rigidity for compact non-positively curved manifolds, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI (in press).
  • [26] -, The lower algebraic $ K$-theory of virtually $ \infty $-cyclic groups, submitted for publication.
  • [27] S. Gersten, On spectrum of algebraic $ K$-theory, Bull. Amer. Math. Soc. 78 (1972), 216-219. MR 0299657 (45:8705)
  • [28] T. Goodwillie, unpublished.
  • [29] A. Hatcher, Concordance spaces, higher simple homotopy theory, and applications, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, RI, (1978) pp. 2-21. MR 520490 (80f:57014)
  • [30] W.-c. Hsiang, Geometric applications of algebraic $ K$-theory, Proc. Internat. Congress Math. Warsaw, vol. 1 (1983), pp. 99-118. MR 804679 (87g:57034)
  • [31] -, Borel's conjecture, Novikov's conjecture and the $ K$-theoretic analogue, World Scientific book, Singapore.
  • [32] B. Hu, Ph.D thesis, SUNY at Stony Brook, 1989.
  • [33] -, A P L geometric study of algebraic $ K$-theory, Trans. Amer. Math. Soc. (to appear).
  • [33a] -, Whitehead groups of finite polyhedra with non-positive curvature, J. Differential Geom. (to appear).
  • [33b] -, unpublished.
  • [34] I. M. James, Ex-Homotopy theory, Illinois J. Math. 15 (1971), 324-337. MR 0296945 (45:6004)
  • [35] L. E. Jones, The non-simply connected characteristic variety theorem, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 131-140.
  • [36] R. C. Kirby and L. C. Seibenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Ann. of Math. Stud., vol. 88, Princeton Univ. Press, Princeton, NJ, 1977. MR 0645390 (58:31082)
  • [37] G. D. Mostow, Equivariant embeddings in Euclidean space, Ann. of Math. (2) 40 (1957), 432-446. MR 0087037 (19:291c)
  • [38] A. Nicas, On higher Whitehead groups of a Bieberbach group, Trans. Amer. Math. Soc. 287 (1985), 853-859. MR 768746 (86f:18018a)
  • [39] -, Induction theorems for groups of homotopy manifold structures, Mem. Amer. Math. Soc. 267 (1982). MR 668807 (83i:57026)
  • [40] E. Pedersen and C. Weibel, A non-connective delooping of algebraic $ K$-theory, Topology, Lecture Notes in Math., vol. 1126, Springer-Verlag, Berlin-Heidelberg-New York, 1985, pp. 166-181. MR 802790 (87b:18012)
  • [41] R. S. Palais, Imbedding of compact differentiable transformations groups in orthogonal representations, J. Math. and Mech. 6 (1957), 673-678. MR 0092927 (19:1181e)
  • [42] M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 0507234 (58:22394a)
  • [43] A. Ranicki, Algebraic $ L$-theory II: Laurent extensions, Proc. London Math. Soc. 27 (1973), 126-158. MR 0414662 (54:2760b)
  • [44] D. Sullivan, Lecture notes on the characteristic variety theorem, preprint. MR 0285012 (44:2236)
  • [45] A. Selberg, On discontinuous groups in higher dimensional symmetric spaces, International Colloquium on Function Theory, Tata Inst. of Fund Research, Bombay, 1960, pp. 147-164. MR 0130324 (24:A188)
  • [46] D. Quillen, Higher algebraic $ K$-theory. I, Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin-Heidelberg-New York, 1973, pp. 85-165. MR 0338129 (49:2895)
  • [47] F. Quinn, A geometric formulation of surgery, Topology of Manifolds, Proc. 1969 Georgia Topology Conf., Markham Press, Chicago, IL, 1970, pp. 500-511. MR 0282375 (43:8087)
  • [48] -, Ends of maps. II, Invent. Math. 68 (1982), 353-424. MR 669423 (84j:57011)
  • [49] -, Assembly maps in bordism type theories, preprint.
  • [50] -, Algebraic $ K$-theory of poly-(finite or cyclic) groups, Bull. Amer. Math. Soc. 12 (1985), 221-226. MR 776473 (86e:18015)
  • [51] -, Applications of topology with control, Proc. Internat. Congress of Math. (Berkeley, CA, 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 598-606. MR 934261 (89g:57049)
  • [52] J. Wagoner, Delooping classifying spaces in algebraic $ K$-theory, Topology 11 (1972), 349-370. MR 0354816 (50:7293)
  • [53] F. Waldhausen, Algebraic $ K$-theory of generalized free products, Ann. of Math. (2) 108 (1978), 135-256. MR 0498807 (58:16845a)
  • [54] -, 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)
  • [55] C. T. C. Wall, Surgery on compact manifolds, Academic Press, New York, 1971. MR 0431216 (55:4217)
  • [56] J. A. Wolf, Spaces of constant curvature, Publish or Perish, Berkeley, CA, 1977.
  • [57] M. Yamasaki, $ L$-groups of crystallographic groups, Invent. Math. 88 (1987), 571-602. MR 884801 (88c:57017)
  • [58] -, $ L$-groups of certain virtually solvable groups, Topology Appl. 33 (1989).
  • [59] H. Zassenhaus, Über einen Algorithmus Bestimmung der Raumgruppen, Comment. Math. Helv. 21 (1948), 117-141. MR 0024424 (9:491e)
  • [60] C. A. Weibel, Mayer-Vietoris sequences and module structures on $ N{K_ * }$, Algebraic $ K$-theory, Evanston 1980, Lecture Notes in Math., vol. 854, 1981. MR 618317 (82k:18010)

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DOI: https://doi.org/10.1090/S0894-0347-1993-1179537-0
Article copyright: © Copyright 1993 American Mathematical Society

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