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Pseudo-immersions of oriented surfaces with one boundary component into the plane

Published online by Cambridge University Press:  04 November 2009

Minoru Yamamoto
Affiliation:
Department of Science, Kurume National College of Technology, Komorino 1-1-1, Kurume City, Fukuoka 830–8555, Japan, (minomoto@kurume-nct.ac.jp)
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Abstract

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Let M be a compact connected oriented surface with exactly one boundary component. A pseudo-immersion of M into the plane is a smooth map such that it has only fold singularities and is an orientation-preserving immersion near the boundary of M. For a pseudo-immersion we study the relation between the winding number of the boundary curve and the number of the singular set components.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009