Vassiliev invariants of knots in a spatial graph

Yoshiyuki Ohyama*, Kouki Taniyama

*この研究の対応する著者

研究成果査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)191-205
ページ数15
ジャーナルPacific Journal of Mathematics
200
1
DOI
出版ステータスPublished - 2001 9
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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