Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T14:00:34.171Z Has data issue: false hasContentIssue false
  • English
  • Français

Linking spheres

Published online by Cambridge University Press:  24 October 2008

D. B. A. Epstein
D. B. A. Epstein
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Andrews and Curtis have shown (1) that one can embed two Sn's in En+2 for n = 2, in such a way that one sphere cannot be shrunk to a point in the residue space of the other. In this paper the result is shown to be true for any n ≥ 1. (The result is obvious for n = 1.) The method is to calculate the appropriate homotopy group of the residue space of one sphere, and to show that the embedding of the other sphere represents a non-zero element of the group. The two spheres can both be embedded analytically.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 3 , July 1960 , pp. 215 - 219
Copyright
Copyright © Cambridge Philosophical Society 1960

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)Andrews, J. J. and Curtis, M. L. Knotted 2-spheres in the 4-sphere (to appear).Google Scholar
(2)Artin, E.Abh. Math. Sem. Univ. hamburg 4 (1925), 174–7.CrossRefGoogle Scholar
(3)Papakyrlakopoulos, C. D.On Dehn's lemma and the asphericity of knots. Ann. Math., Princeton, 66 (1957), 1–26.CrossRefGoogle Scholar