Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-03T02:44:05.702Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on 3-fold branched coverings of S3

Published online by Cambridge University Press:  24 October 2008

José María Montesinos
José María Montesinos
Affiliation:
Universidad de Zaragoza, Spain
Get access Rights & Permissions [Opens in a new window]

Extract

H. Hilden(3, 4) and the author(9,10) proved independently the following result:

Theorem 1. Each closed, orientable 3-manifold is a 3-fold, dihedral covering of S3, branched over a knot.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 321 - 325
Copyright
Copyright © Cambridge Philosophical Society 1980

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)Fox, R. H. Some problems in knot theory. Topology of 3-manifolds, ed. Fort, M. K., Prentice Hall, 1962.Google Scholar
(2)Hempel, J. Construction of orientable 3-manifolds. Topology of 3-manifolds, ed. Fort, M. K., Prentice Hall, 1962.Google Scholar
(3)Hilden, H.Every closed, orientable 3-manifold is a 3-fold branched covering space of S 3. Bull. Amer. Math. Soc. 80 (1974), 1243–4.CrossRefGoogle Scholar
(4)Hilden, H.Three-fold branched coverings of S 3. Amer. J. Math. 98 (1976), 989–997.Google Scholar
(5)Hilden, H. and Montesinos, J.A method of constructing 3-manifolds and its application to the computation of the μ-invariant. Proc. of Symposia in Pure Math. A.M.S. Publications 32 (1978), 51–69.Google Scholar
(6)Kirby, R.A calculus for framed links in S 3. Inventions Math. 45 (1978), 35–56.CrossRefGoogle Scholar
(7)Lickorish, W. B.R. A representation of orientable combinatorial 3-manifolds. Ann. of Math. 76 (1962), 531–540.CrossRefGoogle Scholar
(8)Lickorish, W. B. R.A finite set of generators for the homeotopy group of a 2-manifold. Proc. Cambridge Philos. Soc. 60 (1964), 769–78.Google Scholar
Corrigendum Lickorish, W. B. R.A finite set of generators for the homeotopy group of a 2-manifold. Proc. Cambridge Philos. Soc. 62 (1966), 679–81.Google Scholar
(9)Montesinos, J.A representation of closed, orientable 3-manifolds as 3-fold branched coverings of S 3. Bull. Amer. Math. Soc. 80 (1974), 845–6.CrossRefGoogle Scholar
(10)Montesinos, J.Three-manifolds as 3-fold branched covers of S 3. Quarterly J. Math. Oxford (2), 27 (1976), 85–94.Google Scholar
(11)Montesinos, J.4-manifolds, 3-fold covering spaces and ribbons. Trans. Amer. Math. Soc. 245 (1978), 453–467.CrossRefGoogle Scholar
(12)Wallace, A. D.Modifications and cobounding manifolds. Canad. J. Math. 12 (1960), 503–528.Google Scholar