Constructions of round fold maps on C^∞ bundles

2013/05/08 by Naoki Kitazawa, Kitazawa, Naoki
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1305.1708

openalex publication_date 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes special generic maps on spheres and such maps have been constructed on smooth bundles over standard spheres of dimensions larger than 1 and connected sums of smooth bundles over standard spheres of dimensions larger than 1 whose fibers are standard spheres, for example, in previous studies by the author. In this paper, we obtain round fold maps and the diffeomorphism types of their source manifolds which do not appear in these studies in new manners.

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