English

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