No Access

A NOTE ON THE INDEPENDENCE OF REIDEMEISTER MOVES

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

Search for more papers by this author

and

HONGZHU GAO

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0218216512200015Cited by:2 (Source: Crossref)

Abstract

In this paper, from the viewpoint of quandle construction we prove that for any link type L and any diagram of it, there exists another diagram of L such that these two diagrams are Ω₁-dependent, Ω₂-dependent and Ω₃-dependent.

Keywords:

AMSC: 57M25

References

T. J. Hagge, Proc. Amer. Math. Soc. 134, 295 (2006). Crossref, Web of Science, Google Scholar
D. Joyce, J. Pure Appl. Algebra 23, 37 (1982). Crossref, Web of Science, Google Scholar
X. S. Lin, Acta Math. Sin. 17, 361 (2001). Crossref, Web of Science, Google Scholar
V. Manturov , Knot Theory ( Chapman & Hall/CRC , 2004 ) . Crossref, Google Scholar
S. V. Matveev, Math. USSR Sbornik. 47, 73 (1984). Crossref, Google Scholar
O. Östlund, J. Knot Theory Ramifications 10(8), 1215 (2001). Link, Web of Science, Google Scholar
K. Reidemeister, Abh. Math. Sem. Univ. Hamburg. 5, 24 (1927). Crossref, Google Scholar
B. Trace, Proc. Amer. Math. Soc. 89, 722 (1983). Crossref, Web of Science, Google Scholar