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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 95, Issue 1
  • January 1984, pp. 55-60

On Wh3 of a Bieberbach group

  • Andrew J. Nicas (a1)
  • DOI:
  • Published online: 24 October 2008

A closed aspherical manifold is a closed manifold whose universal covering space is contractible. There is the following conjecture concerning the algebraic K-theory of such manifolds:

Conjecture. Let Γ be the fundamental group of a closed aspherical manifold. Then Whi(Γ) = 0 for i ≥ 0 where Whi(Γ) is the i-th higher Whitehead group of Γ.

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[1] D. Bubghelea and R. Lashof . The homotopy type of the space of diffeomorphisms II. Trans. Amer. Math. Soc. 196 (1974), 3750.

[2] D. Bubghelea and R. Lashof . Stability of concordances and the suspension homo-morphism. Ann. of Math. 105 (1977), 449472.

[3] D. Bubghelea , R. Lashof and M. Rothenbebg . Groups of Automorphisms of Manifolds. Lecture Notes in Math. vol. 473 (Springer Verlag, 1975).

[5] F. Farrell and W.-C. Hsiang . The topological Euclidean space form problem. Invent. Math. 45 (1978), 181192.

[8] D. Gottlieb . A certain subgroup of the fundamental group. Amer. J. Math. 87 (1965), 840856.

[11] W.-C. Hsiang and R. Shabpe . Parametrized surgery and isotopy. Pacific J. Math. 67 (1976), 401459.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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