Delta link-homotopy on spatial graphs.

Ryo Nikkuni

Revista Matemática Complutense (2002)

  • Volume: 15, Issue: 2, page 543-570
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Nikkuni, Ryo. "Delta link-homotopy on spatial graphs.." Revista Matemática Complutense 15.2 (2002): 543-570. <http://eudml.org/doc/44366>.

@article{Nikkuni2002,
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.},
author = {Nikkuni, Ryo},
journal = {Revista Matemática Complutense},
keywords = {Homotopía; Inmersiones; Teoría de grafos; Grafo espacial; Nudos topológicos; spatial graph; delta vertex-homotopy; delta edge-homotopy; invariant; balanced weight; Conway polynomial; Jones polynomial},
language = {eng},
number = {2},
pages = {543-570},
title = {Delta link-homotopy on spatial graphs.},
url = {http://eudml.org/doc/44366},
volume = {15},
year = {2002},
}

TY - JOUR
AU - Nikkuni, Ryo
TI - Delta link-homotopy on spatial graphs.
JO - Revista Matemática Complutense
PY - 2002
VL - 15
IS - 2
SP - 543
EP - 570
AB - 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.
LA - eng
KW - Homotopía; Inmersiones; Teoría de grafos; Grafo espacial; Nudos topológicos; spatial graph; delta vertex-homotopy; delta edge-homotopy; invariant; balanced weight; Conway polynomial; Jones polynomial
UR - http://eudml.org/doc/44366
ER -

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