Weight systems for Milnor invariants
نویسنده
چکیده
We use Polyak’s skein relation to give a new proof that Milnor’s string link invariants μ12...n are finite type invariants, and to develop a recursive relation for their associated weight systems. We show that the obstruction to the triviality of these weight systems is the presence of a certain kind of spanning tree in the intersection graph of a chord diagram.
منابع مشابه
Self Delta-equivalence for Links Whose Milnor’s Isotopy Invariants Vanish
For an n-component link, Milnor’s isotopy invariants are defined for each multi-index I = i1i2...im (ij ∈ {1, ..., n}). Here m is called the length. Let r(I) denote the maximum number of times that any index appears in I. It is known that Milnor invariants with r = 1, i.e., Milnor invariants for all multi-indices I with r(I) = 1, are link-homotopy invariant. N. Habegger and X. S. Lin showed tha...
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We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length ≤ k are all zero into a link with vanishing Milnor invariants of length ≤ 2k+1, and we provide formulas for the first non-vanishing ones. As a consequence, we obtain statements relating...
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It has long been known that a Milnor invariant with no repeated index is an invariant of link homotopy. We show that Milnor’s invariants with repeated indices are invariants not only of isotopy, but also of self Ck-moves. A self Ck-move is a natural generalization of link homotopy based on certain degree k clasper surgeries, which provides a filtration of link homotopy classes.
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تاریخ انتشار 2008