Higher Whitehead groups of certain bundles over Seifert manifolds

Authors:
A. J. Nicas and C. W. Stark

Journal:
Proc. Amer. Math. Soc. **91** (1984), 1-5

MSC:
Primary 18F25; Secondary 57T20

MathSciNet review:
735551

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Abstract: Vanishing results for are obtained when is a closed aspherical manifold which is the total space of a bundle over an insufficiently large Seifert manifold with infinite fundamental group of hyperbolic type. Allowable fibers include Riemannian flat manifolds and closed aspherical manifolds with poly- fundamental groups. Corollaries. concern the homotopy groups of the group of self-homeomorphisms of .

**[DI]**R. Keith Dennis and Kiyoshi Igusa,*Hochschild homology and the second obstruction for pseudoisotopy*, Algebraic 𝐾-theory, Part I (Oberwolfach, 1980) Lecture Notes in Math., vol. 966, Springer, Berlin-New York, 1982, pp. 7–58. MR**689365****[Dr]**Andreas W. M. Dress,*Induction and structure theorems for orthogonal representations of finite groups*, Ann. of Math. (2)**102**(1975), no. 2, 291–325. MR**0387392****[FH1]**F. T. Farrell and W. C. Hsiang,*The topological-Euclidean space form problem*, Invent. Math.**45**(1978), no. 2, 181–192. MR**0482771****[FH2]**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****[FH3]**F. T. Farrell and W. C. Hsiang,*Topological characterization of flat and almost flat Riemannian manifolds 𝑀ⁿ (𝑛̸=3,4)*, Amer. J. Math.**105**(1983), no. 3, 641–672. MR**704219**, 10.2307/2374318**[HS]**W. C. Hsiang and R. W. Sharpe,*Parametrized surgery and isotopy*, Pacific J. Math.**67**(1976), no. 2, 401–459. MR**0494165****[KS]**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****[N]**Andrew J. Nicas,*Induction theorems for groups of homotopy manifold structures*, Mem. Amer. Math. Soc.**39**(1982), no. 267, vi+108. MR**668807**, 10.1090/memo/0267**[N2]**-,*On**of a Bieberbach group*, Topology (to appear).**[N3]**-,*On**of a Bieberbach group*, Math. Proc. Cambridge Philos. Soc. (to appear).**[O]**Peter Orlik,*Seifert manifolds*, Lecture Notes in Mathematics, Vol. 291, Springer-Verlag, Berlin-New York, 1972. MR**0426001****[P]**Steven P. Plotnick,*Vanishing of Whitehead groups for Seifert manifolds with infinite fundamental group*, Comment. Math. Helv.**55**(1980), no. 4, 654–667. MR**604721**, 10.1007/BF02566714**[S]**Christopher W. Stark,*Structure sets vanish for certain bundles over Seifert manifolds*, Trans. Amer. Math. Soc.**285**(1984), no. 2, 603–615. MR**752493**, 10.1090/S0002-9947-1984-0752493-3**[SW]**Richard G. Swan,*𝐾-theory of finite groups and orders*, Lecture Notes in Mathematics, Vol. 149, Springer-Verlag, Berlin-New York, 1970. MR**0308195****[W]**Friedhelm Waldhausen,*Algebraic 𝐾-theory of generalized free products. I, II*, Ann. of Math. (2)**108**(1978), no. 1, 135–204. MR**0498807**

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DOI:
https://doi.org/10.1090/S0002-9939-1984-0735551-4

Article copyright:
© Copyright 1984
American Mathematical Society