Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T07:43:20.309Z Has data issue: false hasContentIssue false
  • English
  • Français

On even-dimensional fibred knots obtained by plumbing

Published online by Cambridge University Press:  24 October 2008

Daniel Lines
Daniel Lines
Affiliation:
Institut de mathématiques, Université de Neuchâtel, Switzerland
Get access Rights & Permissions [Opens in a new window]

Extract

In this article we extend the study of ‘plumbing’ initiated in [10] to the case of fibred even-dimensional knots. Plumbing is a geometric operation on the fibre-surfaces of two fibred knots of the same dimension that produces another such knot.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 117 - 131
Copyright
Copyright © Cambridge Philosophical Society 1986

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]Berwick, W.. Integral bases. Cambridge Tracts 22. (Cambridge University Press, 1927).Google Scholar
[2]Haefliger, A.. Plongements différentiables de variétés dans variétés. Comment. Math. Helv. 36 (1962), 47–82.CrossRefGoogle Scholar
[3]Kearton, C.. An algebraic classification of certain simple even dimensional knots. Trans. Amer. Math. Soc. 276 (1983), 1–53.Google Scholar
[4]Kearton, C.. Simple spun knots. Topology 23 (1984), 91–95.CrossRefGoogle Scholar
[5]Kervaire, M.. Les noeuds de dimensions supérieures. Bull. Soc. Math. France 93 (1965), 225–271.Google Scholar
[6]Kervaire, M. and Weber, C.. A survey of multidimensional knots. Knot Theory (Proceedings, Plans-sur-Bex 1977), Lecture Notes in Mathematics 685 (Springer-Verlag, 1978).Google Scholar
[7]Kojima, S.. A classification of some even dimensional fibred knots. J. Fac. Science Univ. of Tokyo Sec 1A 24 (1977), 671–683.Google Scholar
[8]Levine, J.. Unknotting theorems in codimension 2. Topology 4 (1965), 9–16.Google Scholar
[9]Levine, J.. An algebraic classification of some knots of codimension two. Comment. Math. Helv. 45 (1970), 185–198.Google Scholar
[10]Lines, D.. On odd dimensional fibred knots obtained by plumbing and twisting. London Math. Soc. (in the Press).Google Scholar
[11]Morton, H.. Fibred knots with a given Alexander polynomial. Noeuds, Tresses et Singularity (Séminaire des Plans-sur-Bex 1982), Monographic 31, l'Enseignement Mathématique. Genève (1983), 204–222.Google Scholar
[12]Smale, S.. On the structure of manifolds. Amer. J. Math. 84 (1962), 387–399.CrossRefGoogle Scholar
[13]Wall, C. T. C.. Classification problems in differential topology I. Topology 2 (1963), 253–261.CrossRefGoogle Scholar
[14]Whitehead, G.. Elements of Homotopy Theory. Graduate Texts in Mathematics 61 (Springer-Verlag, 1978).Google Scholar