Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-13T08:40:54.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Alexander polynomials of closed 3-braids

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
Department of Pure Mathematics, University of Liverpool
Get access Rights & Permissions [Opens in a new window]

Extract

The knots and links which can arise as the closure of 3-string braids, and their relations to the braids which give rise to them have been studied by Murasugi [5] and others, including Hartley [2] and more recently Przytycki[6]. Three-braids appear to form a rather special class among braids from some points of view [3]; they are also the only group of braids for which Burau's representation is known to be faithful [1]. They are, however, varied enough to provide an interesting range of knots and links on which to test a number of conjectures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 295 - 299
Copyright
Copyright © Cambridge Philosophical Society 1984

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]Birman, J. S.. Braids, Links and Mapping-Class Groups. Annals of Maths. Studies 82 (Princeton University Press, 1974).Google Scholar
[2]Hartley, R.. On the classification of three-braid links. Abh. Math. Sem. Univ. Hamburg 50 (1980), 108–117.CrossRefGoogle Scholar
[3]Morton, H. R.. Closed braids which are not prime knots. Math. Proc. Cambridge Philos. Soc. 86 (1979), 421–426.CrossRefGoogle Scholar
[4]Morton, H. R.. Exchangeable braids. To appear in Proceedings of Sussex Conference 1982.Google Scholar
[5]Murasugi, K.. On Closed 3-braids. Mem. Amer. Math. Soc. 151 (1974).Google Scholar
[6]Przytycki, J.. Incompressibility of surfaces in 3-manifolds. Ph.D. thesis, Columbia University (1981).Google Scholar