Every Reidemeister move is needed for each knot type
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- by Tobias J. Hagge PDF
- Proc. Amer. Math. Soc. 134 (2006), 295-301 Request permission
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
- Vassily Manturov, Knot theory, Chapman & Hall/CRC, Boca Raton, FL, 2004. MR 2068425, DOI 10.1201/9780203402849
- Olof-Petter Östlund, Invariants of knot diagrams and relations among Reidemeister moves, J. Knot Theory Ramifications 10 (2001), no. 8, 1215–1227. MR 1871226, DOI 10.1142/S0218216501001402
- K. Reidemeister. Knotten und gruppen. Abh. Math. Sem. Univ. Hamburg, 1927.
Additional Information
- Tobias J. Hagge
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- Email: thagge@indiana.edu
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 295-301
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-05-07935-9
- MathSciNet review: 2170571