Homotopy on spatial graphs and the Sato-Levine invariant
Geometric Topology
2020-05-19 v3
Abstract
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples of non-splittable spatial graphs up to edge (resp. vertex)-homotopy, all of whose constituent links are link-homotopically trivial.
Cite
@article{arxiv.math/0509003,
title = {Homotopy on spatial graphs and the Sato-Levine invariant},
author = {Thomas Fleming and Ryo Nikkuni},
journal= {arXiv preprint arXiv:math/0509003},
year = {2020}
}
Comments
17 pages,16 figures