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Regular equivalence of special generic maps of manifolds into the plane

Published online by Cambridge University Press:  18 February 2004

MINORU YAMAMOTO
Affiliation:
Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan. e-mail: [email protected]

Abstract

Let $f:M \to N$ be a smooth map of a closed $n$-dimensional manifold $M$ into a $p$-dimensional manifold $N (n \geq p)$. When $f$ has only definite fold singular points, we call it a special generic map. Porto and Furuya introduced the notion of regular equivalence for such maps. In this paper, we define another equivalence relation for special generic maps, called weak regular equivalence and we classify special generic maps up to these equivalences in the case where $M$ is a connected orientable closed $n$-dimensional manifold with $n \geq 3$ and $N$ is the plane. We also show the existence of a pair of special generic maps which are $C^0$ right-left equivalent but are not $C^\infty$ right-left equivalent.

Type
Research Article
Copyright
2004 Cambridge Philosophical Society

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