Homotopy theories of colored links and spatial graphs
Geometric Topology
2023-12-21 v1
Abstract
Two links are called link-homotopic if they are transformed to each other by a sequence of self-crossing changes and ambient isotopies. The notion of link-homotopy is generalized to spatial graphs and it is called component-homotopy. The link-homotopy classes were classified by Habegger and Lin through the classification of the link-homotopy classes of string links. In this paper, we classify colored string links up to colored link-homotopy by using the Habegger-Lin theory. Moreover, we classify colored links and spatial graphs up to colored link-homotopy and component-homotopy respectively.
Keywords
Cite
@article{arxiv.2312.12822,
title = {Homotopy theories of colored links and spatial graphs},
author = {Yuka Kotorii and Atsuhiko Mizusawa},
journal= {arXiv preprint arXiv:2312.12822},
year = {2023}
}
Comments
20 pages, 18 figures