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A 3-manifold which is not a product

Published online by Cambridge University Press:  24 October 2008

D. B. A. Epstein  and
G. P. Scott
D. B. A. Epstein
Affiliation:
University of Warwick and University of Liverpool
G. P. Scott
Affiliation:
University of Warwick and University of Liverpool
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Extract

The purpose of this note is to construct a non-compact 3-manifold M with the following properties:

(i) M is orientable and irreducible

(ii) ∂M is connected and compact and its inclusion in M is a homotopy equivalence

(iii) M is not homeomorphic to ∂M × R+.

(Throughout this paper, all manifolds will be PL and all embeddings will be PL and locally flat.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 445 - 448
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Alexander, J. W.On the subdivision of 3-space by a polyhedron. Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 6–8.CrossRefGoogle ScholarPubMed
(2)Epstein, D. B. A.Ends, topology of 3-manifolds (Prentice-Hall, 1962), 110–117.Google Scholar
(3)Whitehead, J. H. C.A certain open manifold whose group is unity. Quart. J. Math. (Oxford) 6 (1935), 268–279.CrossRefGoogle Scholar