2004/12/13 by Yoshifumi Ando, Ando, Yoshifumi
Mathematics · #57R45 #57R90 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57R45 #msc:57R90
paper · pdf · doi:10.48550/arxiv.math/0412234
26pages
arxiv created 2004/12/13 · openalex publication_date 2004/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N and P be smooth closed manifolds of dimensions n and p respectively. Given a Thom-Boardman symbol I, a smooth map f:N→ P is called an ΩI-regular map if and only if the Thom-Boardman symbol of each singular point of f is not greater than I in the lexicographic order. We will represent the group of all cobordism classes of ΩI-regular maps of n-dimensional closed manifolds into P in terms of certain stable homotopy groups. As an application we will study the relationship among the stable homotopy groups of spheres, the above cobordism group and higher singularities.