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Nilpotent groups and compact 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Charles Thomas
Charles Thomas
Affiliation:
Cornell University
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Extract

The purpose of this paper is to give a complete list of those nilpotent groups which can be the fundamental groups of connected, closed, compact but possibly non-orientable 3-manifolds. The starting point is the following theorem of Reidmeister, which is given a neat proof in (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 303 - 306
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Epstein, D. B. A.On finite presentations of groups and 3-manifolds. Quart. J. Math. Oxford Ser. 12 (1961), 205–12.CrossRefGoogle Scholar
(2)Kurosh, A. G.Theory of groups (Chelsea, 1956).Google Scholar
(3)Milnor, J. W.Groups which act on Sn without fixed points. Amer. J. Math 79 (1957), 623–630.CrossRefGoogle Scholar
(4)Whitehead, J. H. C.On finite cocycles and the sphere theorem. Colloq. Math 6 (1958), 271–281.CrossRefGoogle Scholar