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Abstract: We consider the operation of Whitehead double on a component of a link andstudy the behavior of Milnor invariants under this operation. We show that thisoperation turns a link whose Milnor invariants of length < k are all zero intoa link with vanishing Milnor invariants of length < 2k, and we provide formulasfor the first non-vanishing ones.As a consequence, we obtain statements relating the notions of link-homotopyand self Delta-equivalence via the Whitehead double operation. By using ourresult, we show that a Brunnian link L is link-homotopic to the unlink if andonly if a link L with a single component Whitehed doubled is selfDelta-equivalent to the unlink.

Author: Jean-Baptiste Meilhan, Akira Yasuhara

Source: https://arxiv.org/


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