ar X iv : 0 70 4 . 30 93 v 1 [ m at h . G T ] 2 3 A pr 2 00 7 WHITEHEAD DOUBLE AND MILNOR INVARIANTS
نویسنده
چکیده
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 the notions of link-homotopy and self ∆-equivalence via the Whitehead double operation. By using our result, we show that a Brunnian link L is link-homotopic to the unlink if and only if a link L with a single component Whitehed doubled is self ∆-equivalent to the unlink.
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تاریخ انتشار 2008