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 ≤m>k  m> vanish, then Milnor numbers of length mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864115003855&_mathId=si1.gif&_user=111111111&_pii=S0166864115003855&_rdoc=1&_issn=01668641&md5=405d5777d1ab76931d5ffd049d7e69cc" title="Click to view the MathML source">≤2k+1mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mo>≤mo><mn>2mn><mi>kmi><mo>+mo><mn>1mn>math> are well-defined. Moreover we prove that two clover links whose Milnor numbers of length ≤m>k  m> vanish are equivalent up to edge-homotopy and mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864115003855&_mathId=si2.gif&_user=111111111&_pii=S0166864115003855&_rdoc=1&_issn=01668641&md5=55b4ad4d691d30ef8420eb0e21173e5b" title="Click to view the MathML source">C_2k+1mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><msub><mrow><mi>Cmi>mrow><mrow><mn>2mn><mi>kmi><mo>+mo><mn>1mn>mrow>msub>math>-equivalence if and only if those Milnor numbers of length mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864115003855&_mathId=si1.gif&_user=111111111&_pii=S0166864115003855&_rdoc=1&_issn=01668641&md5=405d5777d1ab76931d5ffd049d7e69cc" title="Click to view the MathML source">≤2k+1mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mo>≤mo><mn>2mn><mi>kmi><mo>+mo><mn>1mn>math> are equal. In particular, we give an edge-homotopy classification of 3-clover links by their Milnor numbers of length ≤3.