2023/12/20 by Yuka Kotorii, Kotorii, Yuka, Atsuhiko Mizusawa +1
Computer Science · Social Sciences · #Data Management and Algorithms #FOS: Mathematics #Geographic Information Systems Studies #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.2312.12822
openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.