Classification of links up to self pass-move

Tetsuo Shibuya, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


A pass-move and a #-move are local moves on oriented links defined by L. H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self #-equivalent) if one can be deformed into the other by pass-moves (resp. #-moves), where none of them can occur between distinct components of the link. These relations are equivalence relations on ordered oriented links and stronger than link-homotopy defined by J. Milnor. We give two complete classifications of links with arbitrarily many components up to self pass-equivalence and up to self #-equivalence respectively. So our classifications give subdivisions of link-homotopy classes.

Original languageEnglish
Pages (from-to)939-946
Number of pages8
JournalJournal of the Mathematical Society of Japan
Issue number4
Publication statusPublished - 2003
Externally publishedYes


  • #-move, pass-move
  • Arf invariant
  • Link-homotopy

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Classification of links up to self pass-move'. Together they form a unique fingerprint.

Cite this