caa a22 4500 38638312X CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500018527 doi S0308210500018527 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500018527 Coghlan Leslie Department of Mathematics, University of Alabama in Birmingham, Birmingham, AL 35294, U.S.A. Tight stable surfaces, II [Elektronische Daten] [Leslie Coghlan] 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. Copyright © Royal Society of Edinburgh 1989 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 213-229 0308-2105 111:3-4<213 1989 111 PRM https://doi.org/10.1017/S0308210500018527 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500018527 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Coghlan Leslie Department of Mathematics, University of Alabama in Birmingham, Birmingham, AL 35294, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 213-229 0308-2105 111:3-4<213 1989 111 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge