Homotopy on spatial graphs and the Sato-Levine invariant
arXiv:math/0509003 · doi:10.1090/S0002-9947-08-04510-8
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.
17 pages,16 figures