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Every Reidemeister move is needed for each knot type

Author(s): Tobias J. Hagge
Journal: Proc. Amer. Math. Soc. 134 (2006), 295-301.
MSC (2000): Primary 57M25
Posted: June 3, 2005
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Abstract | References | Similar articles | Additional information

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.

References:

1.: V. O. Manturov.
Knot Theory.
CRC Press, 2004.
Appendix A. MR 2068425
2.: Olof-Petter Östlund.
Invariants of knot diagrams and relations among Reidemeister moves.
J. Knot Theory Ramifications, 10(8):1215-1227, 2001. MR 1871226 (2002j:57021)
3.: K. Reidemeister.
Knotten und gruppen.
Abh. Math. Sem. Univ. Hamburg, 1927.

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Additional Information:

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

DOI: 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
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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