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December 2014 Constructions of Round Fold Maps on Smooth Bundles
Naoki KITAZAWA
Tokyo J. Math. 37(2): 385-403 (December 2014). DOI: 10.3836/tjm/1422452799

Abstract

In this paper, we construct {\it round fold maps} or {\it stable fold maps} with singular value sets of concentric spheres introduced by the author [11] on smooth bundles over spheres and bundles over more general manifolds. The class of round fold maps includes some {\it special generic maps} on spheres (see [20] for example) and such maps have been constructed on smooth bundles over the standard sphere $S^k$ with $k \geq 2$ and connected sums of smooth bundles over $S^k$ with $k \geq 2$ with fibers diffeomorphic to standard spheres, for example, in previous studies by the author ([10], [12]). In this paper, we obtain round fold maps which do not appear in these studies with information on the diffeomorphism types of their source manifolds in new manners.

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Naoki KITAZAWA. "Constructions of Round Fold Maps on Smooth Bundles." Tokyo J. Math. 37 (2) 385 - 403, December 2014. https://doi.org/10.3836/tjm/1422452799

Information

Published: December 2014
First available in Project Euclid: 28 January 2015

zbMATH: 1337.57061
MathSciNet: MR3304687
Digital Object Identifier: 10.3836/tjm/1422452799

Subjects:
Primary: 57R45
Secondary: 57N15

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

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Vol.37 • No. 2 • December 2014
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