Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T02:53:08.752Z Has data issue: false hasContentIssue false
  • English
  • Français

Cable knots and infinite necklaces of knots

Published online by Cambridge University Press:  17 April 2009

Siegfried Moran
Siegfried Moran
Affiliation:
Institute of MathematicsThe University of KentCanterbury Kent CT2 7NF, United Kingdom
Rights & Permissions [Opens in a new window]

Abstract

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.

The group of an arbitrary companion knot is determined using the theory of braids. This seems to be a new result as far as the resulting group is concerned. The latter part of the paper considers infinite necklaces of knots, their groups and in special cases their Alexander power series.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 17 - 31
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Birman, J.S., Braids, links and mapping class groups (Princeton University Press, 1974).Google Scholar
[2]Burau, W., ‘Über Zopf Invarianten’, Hamburg Abh 9 (1932), 117–124.CrossRefGoogle Scholar
[3]Burde, G. and Zieschang, H., Knots (Gruyter, 1985).Google Scholar
[4]Griffiths, H.B., ‘Infinite products of semigroups and local connectivity’, Proc. London Math. Soc. 6 (1956), 455–485.CrossRefGoogle Scholar
[5]Moran, S., The mathematical theory of knots and braids. An introduction (North-Holland, 1983).Google Scholar
[6]Moran, S., ‘A wild variation of Artin's braids’, Proc NATO ASI Conference on Topics in Knot Theory (Bozhuyuk, M.E., Editor) (Kluwer, 1993), pp. 81–102.Google Scholar
[7]Rolfsen, D., Knots and links (Publish or Perish, 1976).Google Scholar
[8]Seifert, H., ‘On the homology invariants of knots’, Quart. Jour. Math. 1 (1950), 23–32.CrossRefGoogle Scholar