K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11,
author = {Akira Yasuhara},
title = {Brunnian local moves of knots and Vassiliev invariants},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {289-297},
zbl = {1095.57010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11}
}
Akira Yasuhara. Brunnian local moves of knots and Vassiliev invariants. Fundamenta Mathematicae, Tome 189 (2006) pp. 289-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11/