Milnor invariants and edge-homotopy classification of clover links

Kodai Wada

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arXiv · 1506.03922

Milnor invariants and edge-homotopy classification of clover links

Kodai Wada

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Abstract

Given a clover link, we construct a bottom tangle by using a disk/band surface of the clover link. Since the Milnor number is already defined for a bottom tangle, we define the Milnor number for the clover link to be the Milnor number for the bottom tangle and show that for a clover link, if Milnor numbers of length k or less vanish, then Milnor numbers of length 2k+1 or less are well-defined. Moreover we prove that two clover links whose Milnor numbers of length k or less vanish are equivalent up to edge-homotopy and $C_{2k+1}$-equivalence if and only if those Milnor numbers of length 2k+1 or less are equal. In particular, we give an edge-homotopy classification of 3-clover links by their Milnor numbers of length 3 or less.

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BibTeX RIS

Kodai Wada. 2015-06-12. Milnor invariants and edge-homotopy classification of clover links. https://arxiv.org/abs/1506.03922

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