Hostname: page-component-84b7d79bbc-rnpqb Total loading time: 0 Render date: 2024-07-31T07:14:45.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Knots, groups, and spinning

Published online by Cambridge University Press:  18 May 2009

Cherry Kearton
Cherry Kearton
Affiliation:
Department of Mathematical Sciences, Durham University, Durham DH1 3LE, England
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.

In this note we observe how results of Gordon, Luecke, Feustel, and Whitten establish the precise extent to which knowledge of the knot group determines the knot, in both the oriented and the unoriented case. This enables us to say, in terms of the knot group, exactly when two spun knots are the same.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 99 - 100
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Bayer-Fluckiger, E., Kearton, C. and Wilson, S. M. J., Finiteness theorems for conjugacy classes and branched covers of knots, Math. Z. 201 (1989) 485–493.Google Scholar
2.Burde, G. and Zieschang, H., Knots (Walter de Gruyter, 1985).Google Scholar
3.Feustel, C. D. and Whitten, W., Groups and complements of knots, Canad. J. Math. 30 (1978), 1284–1295.CrossRefGoogle Scholar
4.McA, C.. Gordon, A note on spun knots, Proc. Amer. Math. Soc. 58 (1976), 361–362.Google Scholar
5.McA, C.. Gordon, and Luecke, J., Knots are determined by their complements, preprint 1988, University of Texas at Austin.Google Scholar
6.Kearton, C., Simple spun knots, Topology 23 (1984), 91–95.Google Scholar
7.Whitten, W., Knot complements and groups, Topology 26 (1987), 41–44.CrossRefGoogle Scholar