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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
Posted:
June 3, 2005
MathSciNet review:
2170571
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Abstract |
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Abstract: We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister  -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:
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
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
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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