Round fold maps of n-dimensional manifolds into (n-1)-dimensional Euclidean space
Naoki Kitazawa and Osamu Saeki
Journal of Singularities
volume 26 (2023), 1-12
Received: 27 December 2021.
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Abstract:
We determine those smooth closed n-dimensional manifolds with n greater than or equal to 4 which admit round fold maps into (n-1)-dimensional Euclidean space; i.e. fold maps whose critical value sets consist of disjoint spheres of dimension n-2 isotopic to concentric spheres. We also classify such round fold maps up to a certain natural equivalence relation.
2010 Mathematical Subject Classification:
Primary 57R45; Secondary 58K30
Key words and phrases:
round fold map, simple stable map, diffeomorphisms of surfaces, Morse function
Author(s) information:
Naoki Kitazawa
Institute of Mathematics for Industry
Kyushu University
Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
email: n-kitazawa@imi.kyushu-u.ac.jp
Osamu Saeki
Institute of Mathematics for Industry
Kyushu University
Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
email: saeki@imi.kyushu-u.ac.jp