Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T14:52:37.807Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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