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A homological criterion for the realizability of poly-Surface groups

Published online by Cambridge University Press:  24 October 2008

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College, London WC1E 6BT
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Extract

The Realizability Question for poly-Surface groups consists in asking whether, for any poly-Surface group G, one may find a smooth closed aspherical manifold XG with π1(XG)= G. It seems, on present evidence, that the answer is always ‘yes’ [2][3], although in any one case the details may be quite complicated [4].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 89 - 92
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Gbeenberg, L.. Discrete groups of motions. Canad. J. Math. 12 (1960), 415–425.CrossRefGoogle Scholar
[2]Johnson, F. E. A.. On the realisability of poly-Surface groups. J. Pure Appl. Algebra 15 (1979), 235–241.CrossRefGoogle Scholar
[3]Johnson, F. E. A.. Automorphisms of direct products of groups and their geometric realisations. Math. Ann. 263 (1983), 343–364.CrossRefGoogle Scholar
[4]Johnson, F. E. A.. The realisation problem for poly-Surface groups in dimension six. (To appear.)Google Scholar