Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-01T05:42:28.909Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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)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