Vassiliev invariants of knots in a spatial graph

Yoshiyuki Ohyama, Kouki Taniyama

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We show that the Vassiliev invariants of the knots contained in an embedding of a graph G into R3 satisify certain equations that are independent of the choice of the embedding of G. By a similar observation we define certain edge-homotopy invariants and vertex-homotopy invariants of spatial graphs based on the Vassiliev invariants of the knots contained in a spatial graph. A graph G is called adaptable if, given a knot type for each cycle of G, there is an embedding of G into R3 that realizes all of these knot types. As an application we show that a certain planar graph is not adaptable.

Original languageEnglish
Pages (from-to)191-205
Number of pages15
JournalPacific Journal of Mathematics
Volume200
Issue number1
Publication statusPublished - 2001 Sep
Externally publishedYes

Fingerprint

Spatial Graph
Vassiliev Invariants
Knot
Homotopy
Invariant
Graph in graph theory
Planar graph
Cycle
Vertex of a graph

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Vassiliev invariants of knots in a spatial graph. / Ohyama, Yoshiyuki; Taniyama, Kouki.

In: Pacific Journal of Mathematics, Vol. 200, No. 1, 09.2001, p. 191-205.

Research output: Contribution to journalArticle

Ohyama, Yoshiyuki ; Taniyama, Kouki. / Vassiliev invariants of knots in a spatial graph. In: Pacific Journal of Mathematics. 2001 ; Vol. 200, No. 1. pp. 191-205.
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