結び目の円周数による特徴付け

機関リポジトリ Web Site

書誌事項

タイトル別名
  • Characterization of a knot via a circular number
  • ムスビメ ノ エンシュウスウ ニ ヨル トクチョウズケ

この論文をさがす

抄録

A spatial embedding of a graph G is a realization of G into the 3-dimensional Euclidean space R^3. J. H. Conway and C. McA. Gordon proved that every spatial embedding of the complete graph with 7 vertices contains a nontrivial knot. A linear spatial embedding of a graph into R^3 is an embedding which maps each edge to a single straight line segment. In this paper, we actually construct a linear spatial embedding of the complete graph with 2n — 1 (or 2n) vertices which contains the torus knot T(2n — 5, 2) (n ≧ 4). A circular spatial embedding of a graph into R^3 is an embedding which maps each edge to a round arc. We define the circular number of a knot as the minimal number of round arcs in R^3 among such embeddings of the knot. Then we have relations between a circular number and other invariants. We also show that a knot has circular number 3 if and only if the knot is a trefoil knot, and the figure-eight knot has circular number 4.

Departmental Bulletin Paper

application/pdf

収録刊行物

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ