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

Tsukamoto, Tatsuya

doi:10.1090/S0002-9939-99-05221-1

Clasp-pass move and Vassiliev invariants of type three for knots
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by Tatsuya Tsukamoto PDF

Proc. Amer. Math. Soc. 128 (2000), 1859-1867 Request permission

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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