A homotopy classification of two-component spatial graphs up to neighborhood equivalence
Geometric Topology
2020-05-19 v4
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.
Keywords
Cite
@article{arxiv.1212.6629,
title = {A homotopy classification of two-component spatial graphs up to neighborhood equivalence},
author = {Atsuhiko Mizusawa and Ryo Nikkuni},
journal= {arXiv preprint arXiv:1212.6629},
year = {2020}
}
Comments
10 pages, 11 figures