Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T19:01:21.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Conway potential functions for links in ℚ-homology 3-spheres

Published online by Cambridge University Press:  20 January 2009

Steven Boyer  and
Daniel Lines
Steven Boyer
Affiliation:
Département de Mathématiques et D'InformatiqueUniversité du Québec à MontréalC.P. 8888, Succ. A Montréal, H3C 3P8 Québec, Canada
Daniel Lines
Affiliation:
Laboratoire de TopologieUniversité de BourgogneBP 13821004 Dijon Cedex, France
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain a formula relating the Conway potential functions of links in S3 which are connected by a framed surgery operation. Using this formula we extend the theory of Conway potential functions to links in all oriented ℚ-homology 3-spheres.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 53 - 69
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Boyer, S. and Lines, D., Surgery formulae for Casson's invariant and extensions to homology lens spaces, J. Reine Angew. Math. 405 (1990), 181–220.Google Scholar
2.Conway, J. H., An enumeration of knots and links, and some of their algebraic properties, in: Computational problems in abstract algebra (John Leech editor, Pergamon Press, Oxford, 1970), 329–358.Google Scholar
3.Hartley, R., The Conway potential function for links, Comment. Math. Helv. 58 (1983), 365–378.CrossRefGoogle Scholar
4.Hillman, J., Alexander ideals of links (Lecture Notes in Math. 895, Springer-Verlag, Berlin-Heidelberg-New York, 1981).CrossRefGoogle Scholar
5.Kirby, R., A calculus for framed links in S3, Invent. Math. 45 (1978), 35–56.Google Scholar
6.Rolfsen, D., Knots and links (Math. Lecture Series 7, Publish or Perish, Berkeley, Ca., 1976).Google Scholar
7.Seifert, H. and Threlfall, W., A Textbook of Topology (Academic Press, New York, 1980).Google Scholar
8.Turaev, V., Reidemeister torsion in knot theory, Russian Math. Surveys 41 (1986), 97–147.Google Scholar