2024/05/03 by Masato Tanabe, Tanabe, Masato
Computer Science · Mathematics · #32Sxx (Primary) #53D15 (Secondary) #57R42 #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2405.02513
openalex publication_date 2024/05/03 · openalex created_date 2024/05/08 · openalex updated_date 2026/07/28
Our aim is to determine the regular homotopy classes of immersions related to Arnol'd's simple singularities. For every type of simple singularities, we determine the regular homotopy class of the inclusion map of the link into the 5-sphere. We further show that the inclusion map is regularly homotopic to the immersion associated with the corresponding Dynkin diagram, which was constructed by Kinjo. We prove these by computing the complete invariants of the immersions given by Wu and Saeki--Szűcs--Takase. As an application, we also determine the Smale invariants of Kinjo's immersions.