Strong S-equivalence of ordered links

[摘要] 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, that better respects the boundary components of a link;;s Seifert surface, and we 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.

[发布机构] Rice University