A homotopy classification of two-component spatial graphs up to neighborhood equivalence

作者：Mizusawa Atsuhiko^*; Nikkuni Ryo

来源：Topology and Its Applications, 2015, 196: 710-718.

DOI：10.1016/j.topol.2015.05.041

• Spatial graph
• Linking number
• Delta move
• Handlebody-link

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.

• 出版日期2015-12