Clasp-pass moves on knots, links and spatial graphs

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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
Volume122
Issue number3
DOIs
Publication statusPublished - 2002 Aug 16
Externally publishedYes

Fingerprint

Conway Polynomial
Spatial Graph
Knot
Linking number
Invariant
Coefficient
Planar graph
Disjoint
If and only if
Cycle

Keywords

  • Clasp-pass move
  • Delta move
  • Spatial graph

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Clasp-pass moves on knots, links and spatial graphs. / Taniyama, Kouki; Yasuhara, Akira.

In: Topology and its Applications, Vol. 122, No. 3, 16.08.2002, p. 501-529.

Research output: Contribution to journalArticle

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