Regular homotopy classes of links of simple singularities and immersions associated with their Dynkin diagrams

Fuente: arXiv
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Main Author: Tanabe, Masato
Format: Preprint
Published: 2024
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author Tanabe, Masato
author_facet Tanabe, Masato
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_02513
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Regular homotopy classes of links of simple singularities and immersions associated with their Dynkin diagrams
Tanabe, Masato
Geometric Topology
Algebraic Topology
32Sxx (Primary), 57R42, 53D15 (Secondary)
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.
title Regular homotopy classes of links of simple singularities and immersions associated with their Dynkin diagrams
topic Geometric Topology
Algebraic Topology
32Sxx (Primary), 57R42, 53D15 (Secondary)
url https://arxiv.org/abs/2405.02513