Stability of fold maps of manifolds with boundary
type: Item
instance of: scholarly article
title: Stability of fold maps of manifolds with boundary
zbMATH Open document ID: 1048.57017
author: Naoki Shibata
published in: Hokkaido Mathematical Journal
publication date: 2004-03-01T00:00:00Z
review text: Let \(X^m\) be a compact orientable smooth manifold with nonempty boundary and consider \(f:X^m \to Y^n\), \(m \geq n\), a stable smooth map. The singular set is allowed to intersect the boundary. The author characterizes stability of immersions on manifolds with boundary, gives a local form about a fold point (in particular on the boundary) and provides necessary and sufficient conditions for \(f\) with only fold singularities to be stable. Other examples of results about stable maps on manifolds with boundary appeared in \textit{E. von Essen} [Math. Scand. 43, 197--203 (1978; Zbl 0408.58025)], \textit{N. Shibata} [Hiroshima Math. J. 30, No. 3, 415--435 (2000; Zbl 0971.57035) and Kumamoto J. Math. 16, 43--49 (2003; Zbl 1051.58017)]. Examples of results (when \(n=2\) and \(Y^2\) is the plane) in which a requirement is present that the singular set does not intersect the boundary appeared in \textit{H. Levine} [Proc. Am. Math. Soc. 123, No. 8, 2563--2567 (1995; Zbl 0824.57023)].
reviewed by: James G. Timourian
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 58K30
zbMATH DE Number: 2048547
zbMATH Keywords: singularity
zbMATH Keywords: fold point
zbMATH Keywords: stable map
zbMATH Keywords: immersions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350659152
OpenAlex ID: W2115704449
DOI: 10.14492/HOKMJ/1350659152
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description: scientific article; zbMATH DE number 2048547