Whitehead double and Milnor invariants
Geometric Topology
2012-03-01 v2
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.
Cite
@article{arxiv.0704.3093,
title = {Whitehead double and Milnor invariants},
author = {Jean-Baptiste Meilhan and Akira Yasuhara},
journal= {arXiv preprint arXiv:0704.3093},
year = {2012}
}