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arXiv · 0704.3093

Whitehead double and Milnor invariants

Jean-Baptiste Meilhan·Akira Yasuhara
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Abstract

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, and we provide formulas for the first non-vanishing ones. As a consequence, we obtain statements relating the notions of link-homotopy and self Delta-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 Delta-equivalent to the unlink.

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BibTeXRIS

Jean-Baptiste Meilhan, Akira Yasuhara. 2012-02-29. Whitehead double and Milnor invariants. https://arxiv.org/abs/0704.3093

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