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

 

Clasp-pass move and Vassiliev invariants
of type three for knots


Author: Tatsuya Tsukamoto
Journal: Proc. Amer. Math. Soc. 128 (2000), 1859-1867
MSC (1991): Primary 57M25
Published electronically: September 30, 1999
MathSciNet review: 1646209
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Abstract: Recently it has been proved that if and only if two knots $K_1$ and $K_2$ have the same value for the Vassiliev invariant of type two, then $K_1$ can be deformed into $K_2$ by a finite sequence of clasp-pass moves. In this paper, we determine the difference of the values of the Vassiliev invariant of type three between two knots which can be deformed into each other by a clasp-pass move.


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Additional Information

Tatsuya Tsukamoto
Affiliation: Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan; Department of Mathematics, The George Washington University, Washington, D.C. 20052
Email: tatsuya@gwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05221-1
PII: S 0002-9939(99)05221-1
Keywords: Vassiliev invariant, Jones polynomial, clasp-pass move
Received by editor(s): July 31, 1998
Published electronically: September 30, 1999
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society