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Strong S-equivalence of ordered links

Carol Gwosdz Gee
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Abstract

Recently Swatee Naik and Theodore Stanford proved that two S-equivalent knots are related by a finite sequence of doubled-delta moves on their knot diagrams. We show that classical S-equivalence is not sufficient to extend their result to ordered links. We define a new algebraic relation on Seifert matrices, called Strong S-equivalence, and prove that two oriented, ordered links L and L' are related by a sequence of doubled-delta moves if and only if they are Strongly S-equivalent. We also show that this is equivalent to the fact that L' can be obtained from L through a sequence of Y-clasper surgeries, where each clasper leaf has total linking number zero with L.

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Carol Gwosdz Gee. 2004-09-22. Strong S-equivalence of ordered links. https://arxiv.org/abs/math/0409440

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