Full paper in PDF:
$%R. Nikkuni, Delta link-homotopy on spatial graphs, Rev. Mat. Complut. 15 (2002), no. 2, 543-570.%$

Delta Link-Homotopy on Spatial Graphs
Ryo NIKKUNI
Division of Mathematics
Graduate School of Information Sciences
Tohoku University
Aramaki aza Aoba 09
Aoba-ku, Sendai 980-8579 — Japan

Received: April 18, 2001
Revised: March 7, 2002

ABSTRACT

We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the second coefficient of the Conway polynomial and the third derivative at 1  of the Jones polynomial of a knot.

2000 Mathematics Subject Classification: 57M25, 57M15, 05C10.