Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T14:51:04.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Links with alternating diagrams on closed surfaces of positive genus

Published online by Cambridge University Press:  24 October 2008

Chuichiro Hayashi
Chuichiro Hayashi
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Hongo, Tokyo 113, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider links in an orientable 3-manifold M which have an alternating diagram on a closed orientable surface F of positive genus. We see that if the diagram is ‘complex’ enough and if F gives a Heegaard splitting of M, then such a link L is prime and M—L does not contain an essential torus.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 113 - 128
Copyright
Copyright © Cambridge Philosophical Society 1995

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]Adams, C. C.. Toroidary alternating knots and kinks, to appear in Topology.Google Scholar
[2]Menasco, W.. Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984), 37–44.CrossRefGoogle Scholar