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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every Reidemeister move is needed for each knot type


Author: Tobias J. Hagge
Journal: Proc. Amer. Math. Soc. 134 (2006), 295-301
MSC (2000): Primary 57M25
Published electronically: June 3, 2005
MathSciNet review: 2170571
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Abstract: We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister $\Omega_2$-moves. The proof is compatible with known results for the other move types, in the sense that every knot type admits a pair of diagrams that cannot be made identical without using all of the move types.


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Additional Information

Tobias J. Hagge
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: thagge@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07935-9
PII: S 0002-9939(05)07935-9
Received by editor(s): May 20, 2004
Received by editor(s) in revised form: August 18, 2004
Published electronically: June 3, 2005
Additional Notes: The author thanks Charles Livingston, Zhenghan Wang, Scott Baldridge, and Noah Salvaterra for their helpful comments, and Vladimir Chernov for pointing out this problem.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.