Elimination of definite fold II

2017/09/12 by Osamu Saeki, Saeki, Osamu · 2 citations
Computer Science · Mathematics · #57R45 (Primary) 57R35 #58K30 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1709.03804

openalex publication_date 2017/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension strictly greater than 2 into the 2--sphere or into the real projective plane. Our new proof has the advantage that it is not only constructive, but is also algorithmic: the procedures enable us to construct various explicit examples. We also study simple stable maps of 3--manifolds into the 2--sphere without definite fold. Furthermore, we prove the non-existence of singular Legendre fibrations on 3--manifolds, answering negatively to a question posed in our previous paper.

Cited by

• On the number of components of folds of image simple fold maps
• On nonorientable 4--manifolds

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