Proceedings of the American Mathematical Society

Author(s): Tatsuya Tsukamoto
Journal: Proc. Amer. Math. Soc. 128 (2000), 1859-1867.
MSC (1991): Primary 57M25
Posted: September 30, 1999
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Abstract: Recently it has been proved that if and only if two knots

and

have the same value for the Vassiliev invariant of type two, then

can be deformed into

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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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: 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
Posted: September 30, 1999
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society

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