English

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.

Keywords

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

R2 v1 2026-07-22T17:23:58.986Z