Skip to main content
Log in

Knots in the 4-sphere

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. E. Artin,Zur Isotopie zweidimensionaler Flächen in R 4, Abh. Math. Sem. Univ. Hamburg4 (1926), 174–177.

    Article  Google Scholar 

  2. W. Browder,Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc.128 (1967), 155–163.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Cappell,Superspinning and knot complements, inTopology of Manifolds, Markham, Chicago, Ill., 1970, 358–383.

    Google Scholar 

  4. S. E. Cappell andJ. L. Shaneson,There exist inequivalent knots with the same complement, Ann. of Math.103 (1976), 349–353.

    Article  MathSciNet  Google Scholar 

  5. C. H. Giffen,The generalized Smith conjecture, Amer. J. Math.88 (1966), 187–198.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Gluck,The embedding of two-spheres in the four-sphere, Trans. Amer. Math. Soc.104 (1962), 308–333.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. McA. Gordon,Twist-spun torus knots, Proc. Amer. Math. Soc.32 (1972), 319–322.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. McA. Gordon,Some higher-dimensional knots with the same homotopy groups, Quart. J. Math. Oxford24 (1973), 411–422.

    Article  MATH  Google Scholar 

  9. C. McA. Gordon,On the higher-dimensional Smith conjecture, Proc. London Math. Soc.29 (1974), 98–110.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Kato,A concordance classification of PL homeomorphisms of S p × S q, Topology8 (1969), 371–383.

    Article  MATH  MathSciNet  Google Scholar 

  11. R. K. Lashof andJ. L. Shaneson,Classification of knots in codimension two, Bull. Amer. Math. Soc.75 (1969), 171–175.

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Mazur,Symmetric homology spheres, Illinois J. Math.6 (1962), 245–250.

    MATH  MathSciNet  Google Scholar 

  13. H. Seifert,Topologie dreidimensionaler gefaserter Räume, Acta. Math.60 (1933), 147–238.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. W. Sumners,Smooth Z p -actions on spheres which leave knots pointwise fixed, Trans. Amer. Math. Soc.205 (1975), 193–203.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. A. Swarup,A note on higher dimensional knots, Math. Zeit.121 (1971), 141–144.

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Waldhausen,On irreducible 3-manifolds which are sufficiently large, Ann. Math.87 (1968), 56–88.

    Article  MathSciNet  Google Scholar 

  17. J. H. C. Whitehead,On doubled knots, J. London Math. Soc.12 (1937), 63–71.

    Article  MATH  Google Scholar 

  18. E. C. Zeeman,Twisting spun knots, Trans. Amer. Math. Soc.115 (1965), 471–495.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by a Science Research Council Postdoctoral Research Fellowship.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gordon, C.M. Knots in the 4-sphere. Commentarii Mathematici Helvetici 51, 585–596 (1976). https://doi.org/10.1007/BF02568175

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568175

Keywords

Navigation