Milnor invariants and edge-homotopy classification of clover links
Geometric Topology
2015-06-15 v1
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 -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.
Keywords
Cite
@article{arxiv.1506.03922,
title = {Milnor invariants and edge-homotopy classification of clover links},
author = {Kodai Wada},
journal= {arXiv preprint arXiv:1506.03922},
year = {2015}
}