Clasp-pass moves on knots, links and spatial graphs

Kouki Taniyama*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


A clasp-pass move is a local move on oriented links introduced by Habiro in 1993. He showed that two knots are transformed into each other by clasp-pass moves if and only if they have the same second coefficient of the Conway polynomial. We extend his classification to two-component links, three-component links, algebraically split links, and spatial embeddings of a planar graph that does not contain disjoint cycles. These are classified in terms of linking numbers, the second coefficient of the Conway polynomial, the Arf invariant, and the Milnor μ-invariant.

Original languageEnglish
Pages (from-to)501-529
Number of pages29
JournalTopology and its Applications
Issue number3
Publication statusPublished - 2002 Aug 16
Externally publishedYes


  • Clasp-pass move
  • Delta move
  • Spatial graph

ASJC Scopus subject areas

  • Geometry and Topology


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