Hostname: page-component-5cf477f64f-zrtmk Total loading time: 0 Render date: 2025-04-07T06:34:43.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Aspherical manifolds with the Q-homology of a sphere

Published online by Cambridge University Press:  26 February 2010

Andrzej Szczepański
Andrzej Szczepański
Affiliation:
Mathematical Institute, Technical University Gdańsk, ul. Majakowskiego 11/12, 80–952 Gdańsk, Poland.
Get access

Extract

Kan and Thurston, in their paper [5], asked whether each smooth closed manifold other than S2 or RP2 has the same integral homology as a closed aspherical manifold. F. E. A. Johnson in [3], [4] is concerned with the answer to this question when the smooth closed manifold is an n-dimensional sphere Sn. He asked whether there exist aspherical manifolds Xг which have the homology of Sn.

MSC classification

Secondary: 57S30: Discontinuous groups of transformations
Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 291 - 294
Copyright
Copyright © University College London 1983

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

1.Charlap, L. S.. Compact flat Riemannian manifolds I. Ann. Math., 81 (1965), 15–30.CrossRefGoogle Scholar
2.Hantzche, W. and Wendt, W.. Drei dimensionale Euklidische Raumformen. Math. Ann., 110 (1934), 593–611.CrossRefGoogle Scholar
3.Johnson, F. E. A.. Aspherical manifolds of standard linear type. Math. Ann., 255 (1981). 303–316.CrossRefGoogle Scholar
4.Johnson, F. E. A.. Locally symmetric homology spheres and an application of Matsushima's formula. Math. Proc. Camb. Phil. Soc, 91 (1982), 459–465.Google Scholar
5.Kan, D. M. and Thurston, W. P.. Every connected space has the homology K(π, 1). Topology, 15 (1976), 253–258.CrossRefGoogle Scholar
6.Maclane, S.. Homology (Springer, Berlin, Heidelberg, 1963).CrossRefGoogle Scholar
7.Maxwell, G.. Compact Euclidean Space Forms. J. of Alg., 44 (1977), 191–195.CrossRefGoogle Scholar
8.Wolf, J. A.. Spaces of constant curvature (McGraw-Hill Inc., 1967).Google Scholar