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On Wh3 of a Bieberbach group

Published online by Cambridge University Press:  24 October 2008

Andrew J. Nicas
Andrew J. Nicas
Affiliation:
Department of Mathematics, Brandeis University, Waltham, MA 02254
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 55 - 60
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1] Bubghelea, D. and Lashof, R.. The homotopy type of the space of diffeomorphisms II. Trans. Amer. Math. Soc. 196 (1974), 37–50.CrossRefGoogle Scholar
[2] Bubghelea, D. and Lashof, R.. Stability of concordances and the suspension homo-morphism. Ann. of Math. 105 (1977), 449–472.CrossRefGoogle Scholar
[3] Bubghelea, D., Lashof, R. and Rothenbebg, M.. Groups of Automorphisms of Manifolds. Lecture Notes in Math. vol. 473 (Springer Verlag, 1975).CrossRefGoogle Scholar
[4] Dennis, R. K. and Igusa, K.. Hochschild homology and the second obstruction for pseudo- isotopy. Proceedings of the K-theory Conference Oberwolfach 1980 (to appear in Springer Verlag, Lecture Notes in Math.).Google Scholar
[5] Farrell, F. and Hsiang, W.-C.. The topological Euclidean space form problem. Invent. Math. 45 (1978), 181–192.CrossRefGoogle Scholar
[6] Farrell, F. and Hsiang, W.-C.. Topological characterization of flat and almost flat Riemannian manifolds Mn (n ≠ 3, 4). (Preprint.)Google Scholar
[7] Farrell, F. and Hsiang, W.-C.. On the rational homotopy groups of the diffeomorphism groups of discs, spheres, and aspherical manifolds. Proc. Symp. Pure Math. 32 (1978), 3–22.Google Scholar
[8] Gottlieb, D.. A certain subgroup of the fundamental group. Amer. J. Math. 87 (1965), 840–856.CrossRefGoogle Scholar
[9] Hatches, A.. Concordance spaces, higher simple homotopy theory and applications. Proc. Symp. Pure Math 32 (1978), 3–22.CrossRefGoogle Scholar
[10] Hsiang, W.-C. and Jahben, B.. On the homotopy groups of the diffeomorphisms groups of spherical space forms. (Preprint.)Google Scholar
[11] Hsiang, W.-C. and Shabpe, R.. Parametrized surgery and isotopy. Pacific J. Math. 67 (1976), 401–459.CrossRefGoogle Scholar
[12] Igusa, K.. Pseudoisotopy (to appear in Springer Verlag, Lecture Notes in Math.).Google Scholar
[13] Igusa, K.. Stability of Smooth Pseudoisotopy. Aarhus Lecture Notes, 1981.Google Scholar
[14] Nicas, A.. On Wh 2, of a Bieberbach group. (To appear in Topology.)Google Scholar