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Reidemeister's theorem for 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Paul A. Sundheim
Paul A. Sundheim
Affiliation:
Mathematics Department, University of Texas, Austin, Texas 78712, U.S.A.
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Extract

The Reidemeister theorem describes the equivalence of links in terms of diagrams (this theorem was proven in detail by Alexander [1]). A diagram for a link in S3 can be found by projecting the link to any disc recording the over or under crossings. It was shown that two links are equivalent if and only if their diagrams are related by a sequence of so called Reidemeister moves and isotopy in the disc.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 281 - 292
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Alexander, J. W.. On types of knotted curves. Ann. of Math. (2) 28 (1927), 562–567.CrossRefGoogle Scholar
[2]Alexander, J. W.. A lemma on systems of knotted curves. Proc. Acad. Sci. USA 9 (1923) 93–95.CrossRefGoogle ScholarPubMed
[3]Skora, R. K.. Knots and links in 3-manifolds. Preprint (1991).CrossRefGoogle Scholar