Ck-moves on spatial theta-curves and Vassiliev invariants

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The Ck-equivalence is an equivalence relation generated by Ck-moves defined by Habiro. Habiro showed that the set of Ck-equivalence classes of the knots forms an abelian group under the connected sum and it can be classified by the additive Vassiliev invariant of order ≤k-1. We see that the set of Ck-equivalence classes of the spatial θ-curves forms a group under the vertex connected sum and that if the group is abelian, then it can be classified by the additive Vassiliev invariant of order ≤k-1. However the group is not necessarily abelian. In fact, we show that it is nonabelian for k≥12. As an easy consequence, we have the set of Ck-equivalence classes of m-string links, which forms a group under the composition, is nonabelian for k≥12 and m≥2.

Original languageEnglish
Pages (from-to)309-324
Number of pages16
JournalTopology and its Applications
Volume128
Issue number2-3
DOIs
Publication statusPublished - 2003 Feb 15
Externally publishedYes

Fingerprint

Vassiliev Invariants
Equivalence class
Connected Sum
Curve
Equivalence relation
Knot
Abelian group
Strings
Equivalence
Vertex of a graph
Form

Keywords

  • C-move
  • Finite type invariant
  • Spatial theta-curve
  • Vassiliev invariant

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Ck-moves on spatial theta-curves and Vassiliev invariants. / Yasuhara, Akira.

In: Topology and its Applications, Vol. 128, No. 2-3, 15.02.2003, p. 309-324.

Research output: Contribution to journalArticle

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