Constructions of round fold maps on $C^{\infty }$ bundles

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.

arXiv admin note: substantial text overlap with arXiv:1304.0618

References in corpus (1)

• Round fold maps and the topologies and the differentiable structures of manifolds admitting explicit ones

Cited by in corpus (7)

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• Round fold maps on manifolds regarded as the total spaces of linear and more general bundles
• Branched surfaces homeomorphic to Reeb spaces of simple fold maps
• On simple classes of special generic maps and round fold maps and fold maps obtained by composing projections
• 7-dimensional closed simply-connected and spin manifolds having 2nd integral cohomology classes whose squares are not divisible by 2 and stable fold maps on them