Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-16T09:30:31.106Z Has data issue: false hasContentIssue false

On an unlinking theorem

Published online by Cambridge University Press:  24 October 2008

D. W. Sumners
Affiliation:
Florida State University

Extract

An n-link of multiplicity is a smooth embedding of the disjoint union of μ copies of Sn in Sn+2; is said to be trivial if it extends to a smooth embedding of the disjoint union of μ copies of Dn+1. Let , and Cnμ denote the wedge product of μ copies of S1 and (μ – 1) copies of Sn+1. Then clearly, if is trivial, then XCn, where ≃ denotes homotopy equivalence.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1972

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. Ann. of Math. 70 (1959), 565571.CrossRefGoogle Scholar
(2)Andrews, J. J. and Sumners, D. W.On higher-dimensional fibred knots. Trans Amer. Math. Soc. 153 (1971), 415426.CrossRefGoogle Scholar
(3)Artin, E.Zur Isotopic Zweidimensionaler Flachen im R 4. Abh. Math. Sem. Univ. Hamburg 4 (1925), 174177.CrossRefGoogle Scholar
(4)Bing, R. H.Mapping a 3-sphere onto a homotopy 3-sphere. Topology Seminar Wisconsin, 1965 (Ann. of Math. Study no. 60), 8999.Google Scholar
(5)Epstein, D. B. A.Linking spheres. Proc. Cambridge Philos. Soc. 56 (1960), 215219.CrossRefGoogle Scholar
(6)Gutierrez, M. Unlinking spheres in codimension two. Preprint.Google Scholar
(7)Levine, J.Polynomial invariants of knots of codimension two. Ann. of Math. 84 (1966), 537544.CrossRefGoogle Scholar
(8)Parkyriakopoulos, C. D.On Dehn's lemma and the asphericity of knots. Ann. of Math, 66 (1957), 126.CrossRefGoogle Scholar
(9)Smythe, N.Trivial knots with arbitrary projection. J. Austral. Math. Soc. 7 (1967), 481489.CrossRefGoogle Scholar
(10)Wendt, H.Die gordische Auflösung von Knoten. Math. Zeit. 42 (1937), 680696.CrossRefGoogle Scholar