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Tight stable surfaces, II

Published online by Cambridge University Press:  14 November 2011

Leslie Coghlan
Leslie Coghlan
Affiliation:
Department of Mathematics, University of Alabama in Birmingham, Birmingham, AL 35294, U.S.A.
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Synopsis

Kuiper has proved that there is no tight topological immersion of RP2 into E3. Thus any continuous tight map RP2 → E3 has to have singular points. In this note we consider tight C∞-stable maps of RP2 and the torus into E3; i.e. maps with the simplest possible singularities (Whitney pinchpoints) and transversal crossings. We classify the forms that the outer part of such maps can take; we prove also some facts about the inner part. The result about the outer part of C℞-stable tight maps RP2 → E3 establishes the first half of Banchoff's conjectured classification of such mappings.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 213 - 229
Copyright
Copyright © Royal Society of Edinburgh 1989

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