Symmetries of spatial graphs and Simon invariants

• Autorzy: Ryo Nikkuni , Kouki Taniyama
• Języki publikacji: EN

Abstrakty

EN

An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3 + 3 vertices in detail, and determine necessary conditions on linking numbers and Simon invariants for such links and spatial graphs to be symmetric.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57M15: Relations with graph theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 205
• Numer: 3
• Strony: 219-236

Daty

wydano

2009

Twórcy

autor

Ryo Nikkuni

• Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

autor

Kouki Taniyama

• Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku-ku, Tokyo 169-8050, Japan

Identyfikatory

DOI

10.4064/fm205-3-2