Milnor invariants and edge-homotopy classification of clover links

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• 作者：Kodai Wada ^{k.wada@akane.waseda.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Milnor invariant ; Clover link ; Spatial graph ; Edge-homotopy ; Link-homotopy ; CkCk-equivalence
• 刊名：Topology and its Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：196
• 期：part_PA
• 页码：274-289
• 全文大小：515 K

文摘

We define Milnor numbers for clover links and show that for a clover link, if Milnor numbers of length ≤k   vanish, then Milnor numbers of length ≤2k+1$\le 2k+1$ are well-defined. Moreover we prove that two clover links whose Milnor numbers of length ≤k   vanish are equivalent up to edge-homotopy and C_2k+1$C_{2k+1}$-equivalence if and only if those Milnor numbers of length ≤2k+1$\le 2k+1$ are equal. In particular, we give an edge-homotopy classification of 3-clover links by their Milnor numbers of length ≤3.