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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
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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

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References

REFERENCES

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