Milnor invariants of clover links

Kodai Wada*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Levine introduced clover links to investigate the indeterminacy of Milnor invariants of links. He proved that for a clover link, Milnor numbers of length up to 2k + 1 are well-defined if those of length ≤ k vanish, and that Milnor numbers of length at least 2k + 2 are not well-defined if those of length k + 1 survive. For a clover link c with vanishing Milnor numbers of length ≤ k, we show that the Milnor number μc(I) for a sequence I is well-defined by taking modulo the greatest common divisor of the μc(J)′s, where J is any proper subsequence of I obtained by removing at least k + 1 indices. Moreover, if I is a non-repeated sequence of length 2k + 2, the possible range of μc(I) is given explicitly. As an application, we give an edge-homotopy classification of 4-clover links.

Original languageEnglish
Article number1650108
JournalInternational Journal of Mathematics
Issue number13
Publication statusPublished - 2016 Dec 1
Externally publishedYes


  • Milnor invariants
  • based links
  • clover links
  • edge-homotopy
  • link-homotopy
  • spatial graphs

ASJC Scopus subject areas

  • Mathematics(all)


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