A homotopy classification of two-component spatial graphs up to neighborhood equivalence
arXiv:1212.6629 · doi:10.1016/j.topol.2015.05.041
Abstract
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.
10 pages, 11 figures