Whitehead double and Milnor invariants

Details Whitehead double and Milnor invariants Whitehead double and Milnor invariants

2007-04-23

arxiv.org/abs/0704.3093v2

Osaka J. Math. 48 No. 2 (2011), 371-381

Mathematics

Geometric Topology

9 pages, 5 figures. Some minor modifications in this final version

Scientific paper

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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